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Volume of a rectangular prism

Here you will learn about the volume of a rectangular prism, including what it is and how to find it.

Students will first learn about the volume of a rectangular prism as part of geometry in 5 th grade. Students will expand on this knowledge in 6 th grade to include rectangular prisms with fractional dimensions.

Every week, we teach lessons on finding the volume of a rectangular prism to students in schools and districts across the US as part of our online one-on-one math tutoring programs. On this page we’ve broken down everything we’ve learnt about teaching this topic effectively.

What is volume of a rectangular prism?

The volume of a rectangular prism is the amount of space there is within it. Since rectangular prisms are 3 dimensional shapes, the space inside them is measured in cubic units.

\text{Volume of a rectangular prism }=\text { length } \times \text { width } \times \text { height }

For example,

This rectangular prism is made from 24 unit cubes – each side is 1 \, cm . That means the space within the rectangular prism, or the volume, is 24 \, \mathrm{cm}^3.

Even though you can’t see all 24 unit cubes, you can prove there are 24 by thinking about the rectangular prism in parts.

The bottom part of the prism is made up by 2 rows of 4 cubes – or 8 total cubes. The bottom part has a volume of 8 \, \mathrm{cm}^3 .

The other layers of the rectangular prism are exactly the same. Since the height is 3 \, cm , there are 3 layers of cubes. Each layer has a volume of 8 \, \mathrm{cm}^3 , so add them to find the total volume.

Thinking about this further, the volume of a rectangular prism is the area of the base times the height. Consider the same rectangular prism. If you were to hold it up and look at the bottom, it would look like this:

And the height of the prism is 3 \, cm , so 8 \, \mathrm{cm}^2 \times 3 \mathrm{~cm}=24 \mathrm{~cm}^3 .

This is why the formula for the volume of a rectangular prism is:

\text{Volume of a rectangular prism } = \text { length } \times \text { width } \times \text { height }

[FREE] Volume Of A Rectangular Prism Worksheet (Grade 6 to 12)

Use this worksheet to check your grade 6 to 12 students’ understanding of volume of a rectangular prism. 15 questions with answers to identify areas of strength and support!

Common Core State Standards

How does this relate to 5 th grade math and 6 th grade math?

• Grade 5 – Geometry (5.G.C.5b) Apply the formulas V=l \times w \times h and V=b \times h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.
• Grade 6 – Geometry (6.G.A.2) Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l \times w \times h and V = b \times h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

How to calculate the volume of a rectangular prism

In order to find the volume of a rectangular prism with cube units shown:

• Decide how many cubes make up the first layer.
• Find the total of all the layers.

Write the answer and include the units.

In order to calculate the volume of a rectangular prism with the formula:

Write down the formula.

Substitute the values into the formula.

Solve the equation.

Volume of a rectangular prism examples

Example 1: volume of a rectangular prism.

Each cube has a side length of 1 \, inch . Find the volume of the rectangular prism.

If you picked up the prism and looked at the bottom, you would see a 9 by 2 rectangle:

The bottom layer of the rectangular prism is 9 by 2 cubes, so it is made up of 18 inch cubes or 18 \text { inches}{ }^3.

2 Find the total of all the layers.

The height is 2 \, inches , so there are 2 layers of cubes.

Since each layer has a volume of 18 \text { inches}^3 , you can add the volume of each layer to find the total volume.

\begin{aligned} \text { Volume } & = 18 \, \text {inches}^3 + 18 \, \text {inches}^3 \\\\ & = 36 \, \text {inches}^3\end{aligned}

You can also multiply the area of the base ( \text {length } \times \text { width} ) times the \text { height} .

\begin{aligned} \text { Volume } & =18 \text { inches}^2 \times 2 \text { inches } \\\\ & =36 \text { inches}^3 \end{aligned}

3 Write the answer and include the units.

The dimensions of the rectangular prism are in inches, therefore the volume is in cubic inches ( \text { inches}^3. )

\text { Volume }=36 \text { inches}^3

Example 2: volume of a cube

Calculate the volume of this cube.

\text {Volume }=\text { length } \times \text { width } \times \text { height }

Since this is a cube, the length of the rectangular prism, width of the rectangular prism, and height of the rectangular prism are all 6 \,ft :

\text {Volume }=6 \times 6 \times 6

\begin{aligned} & \text {Volume }=6 \times 6 \times 6 \\\\ & \text {Volume }=216 \end{aligned}

The dimensions of the rectangular prism are in feet, therefore the volume is in cubic feet ( ft^3 ).

\text {Volume }=216 \, \mathrm{ft}^3

Example 3: volume of a rectangular prism – different units

Calculate the volume of this rectangular prism.

Notice here that one of the units is in cm and the others are in m . All the units should be the same to calculate the volume.

Change cm to m : 50 \,cm = 0.5 \,m .

Now that all of the measurements are in m, calculate the volume:

\text {Volume }=4 \times 2 \times 0.5

\begin{aligned} & \text {Volume }=4 \times 2 \times 0.5 \\\\ & \text {Volume }=4 \end{aligned}

Since the dimensions of the rectangular prism were calculated in meters, the volume is in cubic meters.

\text {Volume }=4 \, m^3

Example 4: volume of a rectangular prism – fractions

\text {Volume }=9 \times 13 \, \cfrac{2}{3} \, \times 5 \, \cfrac{3}{4}

\begin{aligned} \text {Volume } & =9 \times 13 \, \cfrac{2}{3} \, \times 5 \, \cfrac{3}{4} \\\\ & =\cfrac{9}{1} \, \times \, \cfrac{41}{3} \, \times \, \cfrac{23}{4} \\\\ & =\cfrac{8,487}{12} \\\\ & =707 \, \cfrac{3}{12} \text { or } 707 \, \cfrac{1}{4} \end{aligned}

V=707 \, \cfrac{1}{4} \, f t^3

Example 5: find the length of a rectangular prism given the volume

The rectangular prism below has a square base.

The height of the rectangular prism is 8 \, \cfrac{2}{9} \, m and the volume of the rectangular prism is 33 \, \mathrm{m}^3 .

Find the area of the base.

The volume of the rectangular prism is 33 \, \mathrm{m}^3 and the height is 8 \, \cfrac{2}{9} \, m – fill those into the formula.

\begin{aligned} & 33=l \times w \times 8 \, \cfrac{2}{9} \\\\ & 33=(\text {area of the base}) \times 8 \, \cfrac{2}{9} \end{aligned}

To find the missing area, you can divide 33 by 8 \, \cfrac{2}{9} :

\begin{aligned} & 33 \, \div 8 \, \cfrac{2}{9} \\\\ & =33 \, \div \, \cfrac{74}{9} \\\\ & =\cfrac{33}{1} \, \times \, \cfrac{9}{74} \\\\ & =\cfrac{297}{74} \\\\ & =4 \, \cfrac{1}{74} \end{aligned}

Since the area of the base is calculated by \text {length } \times \text { width} , the measurement is 2D and the units are squared.

The area of the base is 4 \, \cfrac{1}{74} \, m^2.

Example 6: dimensions of a cube given the volume

Find the dimensions of a cube that has a volume of 64 \, \mathrm{mm}^3 .

The only value known is the volume which is 64 \, \mathrm{mm}^3 – fill it into the formula.

64=l \times w \times h

Since the shape is a cube, the length, width and height are all the same. The missing number, when multiplied by itself three times, makes 64 .

Since 64 is even, the number multiplied will also be even. It will also be much smaller than 64 , since it was multiplied 3 times by itself to get to 64 .

With this in mind, start guessing and checking with smaller, even numbers.

Let’s try 2 …

2 \times 2 \times 2=8

Let’s try 4 …

4 \times 4 \times 4=64

The dimensions of the cube are 4 \, \mathrm{mm} \times 4 \, \mathrm{mm} \times 4 \, \mathrm{mm}.

Teaching tips for volume of rectangular prism

• In the beginning, focus on activities and discussions that show the units (cubes) within rectangular prisms and connect such representations to the volume formula.
• Worksheets are easy ways to provide practice problems but be sure to include ones that include word problems or real-life applications of volume.

Easy mistakes to make

• Writing the incorrect units or forgetting to include the units Always include units when recording a measurement. Volume is measured in cubic units. For example, \mathrm{mm}^3, \mathrm{~cm}^3, \mathrm{~m}^3 etc.

• Calculating surface area instead of volume Surface area and volume are different types of measurement – surface area is the total area of the faces and is measured in square units, and volume is the space within the shape and is measured in cubic units.

Related volume lessons

• Volume of a cylinder
• Volume of a hemisphere
• Volume of a sphere
• Volume of a cone
• Volume of a triangular prism
• Volume of a pyramid
• Volume of square pyramid
• Volume formula
• Volume of a prism
• Volume of a cube

Practice volume of a rectangular prism questions

1. Each cube has a side length of 1 \, ft . Find the volume of the rectangular prism.

If you picked up the prism and looked at the bottom, you would see a 6 by 4 rectangle:

The bottom layer of the rectangular prism is 6 by 4 cubes, so it is made up of 24 feet cubes or 24 \, \text {ft}^3.

The height is 4 \, feet , so there are 4 layers of cubes. Since each layer has a volume of 24 \, \text {ft}^3 , you can add the volume of each layer to find the total volume.

\begin{aligned} \text {Volume } & =24 \, f t^3+24 \, f t^3+24 \, f t^3+24 \, f t^3 \\\\ & =96 \, f t^3 \end{aligned}

You can also multiply the area of the base ( \text {length } \times \text { width} ) times the \text {height} .

\begin{aligned} \text {Volume } =24 \, \mathrm{ft}^2 \times 4 \, f t \\\\ & =96 \, \mathrm{ft}^3 \end{aligned}

2. Calculate the volume of the rectangular prism.

\begin{aligned} \text{Volume }&= \text{ length }\times \text{ width }\times \text{ height } \\\\ \text{Volume }&= 12 \times 3 \times 4 \\\\ \text{Volume }&= 144 \, \mathrm{cm}^{3} \end{aligned}

3. Calculate the volume of this rectangular prism.

There are measurements in cm and m , so convert the units before calculating the volume: 380 \, cm to 3.8 \, m .

\begin{aligned} \text{Volume }&= \text{ length }\times \text{ width }\times \text{ height }\\\\ \text{Volume }&= 2.3 \times 2 \times 3.8 \\\\ \text{Volume }&=17.48 \,\mathrm{m}^{3} \end{aligned}

Since the measurements used were in meters, the volume will be in cubic meters.

4. The volume of this rectangular prism is 600 \, cm^{3} . Find the height of the rectangular prism.

Fill in the known values:

\begin{aligned} & 600=8 \times 25 \times h \\\\ & 600=200 \times h \end{aligned}

The missing height times 200 is equal to 600 , so h=3 \, \mathrm{cm} because 200 \times 3=600 .

5. Calculate the volume of the rectangular prism.

\begin{aligned} & \text {Volume }=\text { length } \times \text { width } \times \text { height } \\\\ & \text {Volume }=11 \, \cfrac{3}{4} \, \times 4 \, \cfrac{1}{3} \, \times 3 \, \cfrac{2}{3} \\\\ & \text {Volume }=\cfrac{47}{4} \, \times \, \cfrac{13}{3} \, \times \, \cfrac{11}{3} \\\\ & \text {Volume }=\cfrac{6,721}{36} \\\\ & \text {Volume }=186 \, \cfrac{25}{36} \, \mathrm{ft}^3 \end{aligned}

6. The base of this prism is a square. The volume of the prism is 450 \, \mathrm{cm}^{3} . Find the height of the prism.

Since the base of the prism is a square, the length and the width are both 10 \, cm .

\begin{aligned} & \text {Volume }=\text { length } \times \text { width } \times \text { height } \\\\ & 450=10 \times 10 \times h \\\\ & 450=100 \, h \end{aligned}

The missing height times 100 is equal to 450 , so h=4.5 \, \mathrm{cm} because 100 \times 4.5=450 .

Volume of a rectangular prism FAQs

A cuboid is a three-dimensional shape with 6 rectangular faces, 8 vertices, and 12 edges. It is another name for a rectangular prism.

Volume of a rectangular prism is the area of the base (length times width) times the height of the rectangular prism or l \times w \times h .

No, but the formula for both can be stated as the \text {area of the base } \times \text {height of the prism} . However, since there are different formulas for finding the area of a rectangle and finding the area of a triangle, they are not found with the exact same formula.

Find the area of the six faces and then add them together.

The next lessons are

• Surface area
• Pythagorean theorem
• Trigonometry

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Formula Volume of a Rectangular Prism

How to find the volume of a rectangular cylinder.

This page examines the properties of a rectangular prism such as the image above. A rectangular prism is exactly what it sounds like . It's a 3 dimensional shape with a width, height and a length (or base) such as the 3,2, and 8 this picture .

Rectangular Prism Volume Formula

Practice Problems on Volume of a Rectangular Prism

What is the volume of the rectangular prism with the dimension shown below?

Use the formula for the volume of a cylinder as shown below.

$ V = 2 \cdot 5 \cdot 3 \\ V = 30 $

If the volume of a rectangular prism is 30" 3 and its height is 5", its length is 2", what is its width?

$$ volume = l \cdot w \cdot h \\ 30 = 5 \cdot 2 \cdot w \\ 30 = 10 \cdot w \\ width = \frac{30}{10} = 3\text{"} $$

The volume of a rectangular prism is 125" 3 and its height is 5". Is it possible for all 3 of its dimensions (base, height, width) to be the exact same measurement? Explain.

$$ 5^3 = 125 \\ volume = length \cdot width \cdot height \\ 125 = 5 \cdot 5 \cdot 5 $$

Rectangular prism A has the following dimensions: 2" width, 3" height and 6" base (ie length). On the other hand, rectangular prism B has these dimensions: 1" width, 3" height and 7" base (or length).

Which prism has a greater volume?

$$ \\ volume = length \cdot width \cdot height \\ V = 2 \cdot 3 \cdot 6 = \color{red}{36 \text{ in}^3 } $$

$$ volume = length \cdot width \cdot height \\ V = 1 \cdot 3 \cdot 7 = 21\text{ in}^3 $$

Answer: Prism A

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Volume of rectangular prisms

Geometry word problems.

These grade 5 geometry word problems require the calculation of the volume of rectangular prisms . Some questions will have more than one step and include the addition or subtraction of volumes.

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Volume of a Rectangular Prism Calculator

What is a rectangular prism, what is the formula for the volume of a rectangular prism, how to find the volume of a rectangular prism.

With this volume of a rectangular prism calculator – a.k.a., a box volume calculator – you'll find the volume of any box-shaped container in a blink of an eye. No fuss is required. You need to enter only three values, and we'll calculate the volume for you (though it's not so tricky, you could figure it out yourself 😊).

If you're searching for the definition, check the section What is a rectangular prism . However, if you're still wondering how to find the volume of a rectangular prism, we'll show you step-by-step how to use our calculator on an (almost) real-life example – the volume of a cat 🐈.

If you're looking for the area of a rectangular prism, try our surface area of a rectangular prism calculator , or go to the rectangular prism calculator for an all-in-one rectangular prism tool.

A rectangular prism is a 3D shape with 6 faces, all of which are rectangles . Other names for a rectangular prism are a cuboid , or simply a box .

Every rectangular prism has:

• 8 vertices;
• 12 edges; and

Finding the volume of a rectangular prism is a straightforward task – all you need to do is to multiply the length, width, and height together:

Rectangular prism volume = length × width × height

Where can you use this formula in real life? Let's imagine three possible scenarios:

You bought a fish tank for your golden fish 🐠. It's in a regular box shape, nothing fancy, like a corner bow-front aquarium. If you're wondering how much water you need to fill it, simply use the volume of a rectangular prism formula. It is a similar story for other pets kept in tanks and cages, like turtles or rats – if you want a happy pet, then you should guarantee them enough living space.

The time has come – you've decided that this year you'd like to grow your own carrots 🥕 and salad 🥗. For that, you need to construct a raised bed and fill it with potting soil. But how much dirt should you buy? Well, that's the same question as how to find the volume of a rectangular prism: measure your raised bed, use the formula, and run to the gardening center.

You are going on the vacation of your dreams 🌴. You have to pack your stuff for the three weeks, and you're wondering which suitcase 🧳 will fit more in :

Your good old large suitcase, 30 × 19 × 11 inches; or

The new fancy one, 28 × 21 × 12 inches

That's again the problem solved by the volume of a rectangular prism formula. Solve it manually, or find it using our calculator.

If you're searching for a calculator for other 3D shapes – like e.g. a cube , which is a special case of a rectangular prism – you may want to check out our comprehensive volume calculator . It has a gazillion different shapes! (Fourteen, to be exact.)

Well, now that you know what a rectangular prism is and its volume formula, all the calculations should be a piece of cake! Just measure the three dimensions of your rectangular prism, and use the method from the previous paragraph. Alternatively, you can simply use our box volume calculator.

So, let's have a look at the example – let's calculate the volume of a cat🐈. Yes, a cat, as cats are almost like liquids (they take on the shape of whatever container they are in). Assuming that the cat completely fills a plastic container with dimensions 12 inches × 10 inches × 8 inches:

Input the container's length into the first field of our volume of a rectangular prism calculator. It's 12 inches in our case.

Enter the width of the box . Put 10 inches into the proper field.

Finally, input the height of your container, 8 inches.

And there it is: the volume of a rectangular prism calculator did the job. Now we know that our cat's volume is 960 cubic inches . Isn't that paw esome? 🐾

(Of course, it's a really rough estimate. Take it with a pinch of salt 🧂 or even two pinches.)

So, now that you know your cat's volume, you can go and search for a perfect cardboard box📦 for your pet!

How do I calculate the volume of a rectangular prism?

To find the volume of a rectangular prism, you need to:

• Determine the lengths of the sides : width, length, and height.
• Multiply together the three values from Step 1.
• The result you've got is the volume of your solid.

Don't forget to include the units if it is given! Since it's volume, you need cubic units.

What is the volume of a rectangular prism with sides 2, 5, and 7?

The answer is 70 . To see how to get this result, recall the formula for the volume of a rectangular prism:

volume = length × height × width

Hence, we compute the volume as 2 × 5 × 7 = 70 .

Remember to include the units: for instance, if your measurements are in inches (in), the volume will be in cubic inches (in³).

How do I calculate the volume of a rectangular prism given diagonals?

To determine the volume of a rectangular prism when you know the diagonals of its three faces, you need to apply the formula:

volume = 1/8 × √(a² - b² + c²)(a² + b² - c²)(-a² + b² + c²) ,

where a, b, and c are the diagonals you're given. This formula can be easily derived by using the Pythagorean theorem.

Characteristic polynomial

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Volume of a Rectangular Prism

Introduction.

A rectangular prism is a polyhedron with two congruent and parallel bases.  A rectangular prism is also termed a cuboid. A rectangular prism has six faces and twelve edges. All the six faces are rectangular in shape. Volume is the total amount of space a `3D` object occupies. The total space inside a rectangular prism is called its volume. Picture a rectangular tank that is full of water. In this instance, the capacity of the tank equals the entire amount of water it can hold. Since the rectangular prism is a three-dimensional `(3D)` shape, its volume is expressed in cubic units like `\text{cm}^3`, `\text{m}^3` etc. In this article, we will study the formula for calculating a rectangular prism's volume.

What Do You Mean by Volume of a Rectangular Prism?

The volume of a rectangular prism, also visualized as a rectangular solid or box, refers to the amount of space enclosed by the prism. It represents the total capacity or the total amount of substance that the prism can hold. 

A rectangular prism is a three-dimensional geometric shape characterized by six faces, each of which is a rectangle. These rectangles form three pairs of congruent opposite faces. The length, width, and height of the rectangular prism determine its dimensions. The volume of a rectangular prism is expressed in cubic units, such as cubic centimeters `(\text{cm}^3)` or cubic meters `(\text{m}^3)`, depending on the units used for the dimensions.

It is a fundamental concept in geometry and is widely used in various real-world applications, such as calculating the capacity of containers, determining the amount of material needed for construction or manufacturing, and solving problems in engineering and physics.

Formula for Finding Volume of a Rectangular Prism

The rectangular prism volume formula for finding the volume (\(V\)) of a rectangular prism is:

\( V = l \times w \times h \)

• \( l \) is the length of the rectangular prism.
• \( w \) is the width of the rectangular prism. 
• \( h \) is the height of the rectangular prism.

We multiply the length (\(l\)) by the width (\(w\)) and then by the height (\(h\)) to find the total amount of space enclosed by the prism. This formula represents the product of the three dimensions of the rectangular prism, resulting in a rectangular prism volume measured in cubic units.

We can find numerous things around us that are rectangular prism like a cereal box, a show box, a chest of drawers, a laptop, books, aquarium, etc.

Applications of Volume of a Rectangular Prism

`1`. Packaging and Shipping: Companies use the volume of rectangular prisms to determine the amount of space needed to package and ship products efficiently. Understanding volume helps optimize packaging design and transportation logistics, leading to cost savings and reduced environmental impact.

`2`. Storage Capacity: The volume of a rectangular prism is crucial for determining the storage capacity of containers, warehouses, and storage units. It helps businesses and individuals plan and organize storage space effectively, maximizing utilization while minimizing waste.

`3`. Construction and Architecture: Architects and engineers use volume calculations to design buildings, rooms, and structures. Understanding the volume of materials required, such as concrete, steel, or lumber, helps in estimating costs, planning construction projects, and ensuring structural integrity.

`4`. Manufacturing: Volume calculations are essential in manufacturing processes for determining the quantity of raw materials needed to produce goods. Manufacturers use volume to optimize production efficiency, minimize waste, and maintain consistent quality standards.

`5`. Fluid Mechanics: In fluid dynamics and hydraulic engineering, volume calculations play a vital role in designing pipes, tanks, and reservoirs for storing and transporting liquids. Understanding volume helps ensure proper flow rates, pressure levels, and fluid distribution in hydraulic systems.

`6`. Education and Learning: Volume concepts are taught in mathematics and science education at various levels. Students learn how to calculate volume to solve real-world problems, develop spatial reasoning skills, and understand geometric principles.

`7`. Medical Imaging: In medical imaging technologies such as CT scans and MRI scans, volume measurements are used to quantify the size and shape of organs, tumors, and other anatomical structures. Accurate volume calculations aid in diagnosis, treatment planning, and monitoring of medical conditions.

`8`. Environmental Studies: Volume calculations are used in environmental science and ecology to measure the volume of natural features such as lakes, rivers, and forests. Understanding volume helps researchers assess ecosystem health, monitor changes over time, and develop conservation strategies.

Solved Examples

Example `1`: What is the volume of rectangular prism with the following dimensions:

Length (\( l \)) `= 5` cm,

Width (\( w \)) `= 3` cm,

Height (\( h \)) `= 4` cm.

\( V = 5 \times 3 \times 4 \)

\( V = 60 \text{ cubic centimeters} \)

So, the volume of the rectangular prism is \( 60 \) cubic centimeters.

Example `2`: A rectangular prism has a volume of \( 240 \) cubic meters. If it is `8` meters long and `5` meters wide, what is the height of the prism?

Given: \( V = 240 \) cubic meters, \( l = 8 \) meters, \( w = 5 \) meters.

\( 240 = 8 \times 5 \times h \)

\( 240 = 40h \)

`h = \frac{240}{40}`

\( h = 6 \text{ meters} \)

So, the height of the rectangular prism is \( 6 \) meters.

Example `3`: The area of the base of a rectangular prism is `45` square inches. If the volume of the prism is `225` cubic meters, what is its height?

Given: \( V = 225 \) cubic inches, \( a = 45 \) square inches, \( w = 5 \) inches.

Here `a` is the base area which is \( l \times w \).

\( 225 = a \times h \)

\( 225 = 45h \)

`h = \frac{225}{45}`

\(h = 5 \text{ inches} \)

So, the height of the rectangular prism is \( 5 \) inches.

Example `4`: Find the combined volume of the rectangular prism shown in the composite figure below:

In the composite figure, we have a tall rectangular prism attached to a short rectangular prism. 

Let’s first deal with the long rectangular prism.

\( l = 6 \) in, \( w = 5 \) in and  \( h = 12 \) in.

\( V_1 = l \times w \times h \)

\( V_1 = 6 \times 5 \times 12 \)

\( V_1 = 360 \text{ cubic inches} \)

Now let’s look into the short rectangular prism.

\( l = 14 - 6 = 8 \) in, \( w = 5 \) in and  \( h = 12 - 8 = 4 \) in.

\( V_2 = l \times w \times h \)

\( V_2 = 8 \times 5 \times 4 \)

\( V_2 = 160 \text{ cubic inches} \)

So the combined volume of the composite figure is \(V_1 + V_2\) which is \(360 + 160 = 520 \text{ cubic inches}\).

Example `5`: The volume of a rectangular tank is \( 800 \) cubic centimeters.  If the length of the tank is reduced to `frac{2}{3}` rd of its original length and the height is tripled, what would be the new volume?

Let the original length, width and height of the tank be `l`, `w`, and `h` respectively.

Hence `lwh = 800`

New length of the tank `=\frac{2}{3}l`.

New height of the tank `= 3h`.

New volume of the tank `=\frac{2}{3}l \times w \times 3h`

`=\frac{2}{3} \times 3 \times lwh`

\( =2 \times lwh \)

Substituting `lwh = 800`, we get

New volume  `=2(800) = 1600` cubic centimeters. 

Practice Problems

Q`1`. What is the formula for finding the volume (\(V\)) of a rectangular prism?

• \(V = l + w + h\)
• \(V = l \times w \times h\)
• `V = \frac{l}{w} \times h`
• `V = \frac{l + w}{h}`

Q`2`. A rectangular prism has a length (\(l\)) of `6` meters, a width (\(w\)) of `4` meters, and a height (\(h\)) of `3` meters. What is its volume?

• `36` cubic meters
• `48` cubic meters
• `72` cubic meters
• `96` cubic meters

Answer:  c

Q`3`. If the volume of a rectangular prism is `400` cubic inches and its length is `10` inches, what is its width if the height is `5` inches?

• `16` inches
• `20` inches

Q`4`. Find the base area of a rectangular prism whose volume is `345` cubic inches and height is `15` inches.

• `23` centimeters
• `81` centimeters
• `32` centimeters
• `67` centimeters

Q`5`. The volume of a rectangular tank is \( 550 \) cubic centimeters.  If the length of the tank is doubled and the width is tripled, what would be the new volume?

• `3000` cubic feet
• `3300` cubic feet
• `2800` cubic feet
• `4000` cubic feet

Frequently Asked Questions

Q`1`. What is the volume of a rectangular prism?

Answer: The volume of a rectangular prism refers to the amount of space enclosed by the prism. It is calculated by multiplying the length, width, and height of the prism.

Q`2`. How to find the volume of a rectangular prism?

Answer: To find the volume of a rectangular prism, you multiply its length, width, and height together. The formula for volume of a rectangular prism (\(V\)) is: \(V = l \times w \times h\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

Q`3`. What are the units of volume used for rectangular prisms?

Answer: The units of volume depend on the units used for the dimensions of the rectangular prism. Common units of volume include cubic centimeters `(\text{cm}^3)`, cubic meters `(\text{m}^3)`, cubic inches `(\text{in}^3)`, and cubic feet `(\text{ft}^3)`.

Q`4`. Why is volume important in real-life applications?

Answer: Volume calculations are essential in various fields and everyday tasks. They are used in construction, manufacturing, packaging, transportation, and many other applications to determine capacity, quantify amounts of materials, optimize space, and solve practical problems.

Q`5`. Can the volume of a rectangular prism be negative?

Answer: No, the volume of a rectangular prism cannot be negative. Volume represents a measure of space, and it is always a positive quantity or zero. If the length, width, or height of a rectangular prism is negative, it would indicate an error in measurement or calculation rather than a negative volume.

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Course: 6th grade   >   Unit 10

Volume of a rectangular prism: fractional dimensions.

• Volume by multiplying area of base times height
• Volume with fractions
• How volume changes from changing dimensions
• Volume of a rectangular prism: word problem
• Volume word problems: fractions & decimals

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Volume of a Rectangular Prism Worksheets

Try our engaging volume of rectangular prisms worksheets for grade 5, grade 6, and grade 7, and bolster skills in finding the volume in a step-by-step approach beginning with counting cubes, moving to finding volume of cubes followed by problems to find the volume using area and height expressed as integers, decimals and fractions. Practice finding the volume of L-blocks, convert between units and find the missing parameters as well. Kick-start your preparation with our free worksheets!

Volume of Rectangular Prisms | Integers

Introduce students to find the volume of rectangular prisms with these printable worksheets, presenting the base area and length of the prism as integers. Plug them in V=Base area*height to find the volume.

• Download the set

Volume of Rectangular Prisms | Decimals

Packed here are ample problems to find the volume of rectangular prisms whose base area and one side measure are decimals. Use the known values to work out the volume.

Volume of Rectangular Prisms | Using Side lengths

Instruct 5th grade and 6th grade students to identify the three attributes height, length and width indicated on the rectangular prism and multiply the three to figure out the volume. Easy level deals with values ≤ 20 while moderate level has values ≥ 20.

Volume of Rectangular Prisms | Sides - Decimals

Plug in the measures of the length, height and width expressed as decimals in the formula V=l*w*h and find the volume of each rectangular prism in this set of pdf worksheets.

Volume of Rectangular Prisms | Sides - Fractions

Solve this set of printable volume of rectangular prisms worksheets whose side measures are denoted as fractions. Change the mixed fractions to improper fractions, multiply l*w*h to compute the volume of the prisms.

Volume of Rectangular Prisms | Unit conversion

The dimensions are expressed in different units. Make the units uniform by converting them to the one specified in the answer and then multiply the three to find the volume of the rectangular prisms.

Volume of L-Blocks

Decompose the L-blocks into non-overlapping rectangular prisms and find their volume in these pdf worksheets for grade 6 and grade 7, offering two levels of difficulty classified as easy and moderate based on the range of numbers used.

Volume of L-Blocks | Decimals

Raise the bar with this array of 7th grade worksheets, where the dimensions are expressed as decimals. Split the L-block, determine the volume of individual prisms, sum them up to compute the volume of the L-blocks.

Finding the missing measure

The volume and any two of the three dimensions (height, length or width) are specified. Direct students to rearrange the formula, making the missing measure the subject, assign the known values and solve.

Counting Cubes to find the Volume

Familiarize students with the basics of volume as they begin counting the cubes to determine the volume of each rectangular prism and/or solid block. Practice drawing prisms using the given dimensions as well.

(24 Worksheets)

Volume of Cubes

Catering to the needs of grade 5 through grade 7 children, these volume worksheets add on to your practice in determining the volume of cubes. The dimensions are expressed as integers, decimals and fractions.

(15 Worksheets)

Related Worksheets

» Volume of Triangular Prisms

» Volume of Prisms

» Volume of Rectangular Pyramids

» Volume of Cylinders

» Volume of Composite Shapes

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How to Calculate the Volume of a Rectangular Prism

Last Updated: April 25, 2023 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,283,245 times.

Volume is the amount of three-dimensional space taken up by an object. The computer or phone you're using right now has volume, and even you have volume. Finding the volume of a rectangular prism is actually really easy. Just multiply the length, the width, and the height of the rectangular prism. That's it! This article will walk you through the process step-by-step and show you an example.

• Ex: Length = 5 in.

• Ex: Width = 4 in.

• Ex: Height = 3 in.

• Ex: V = 5 in. * 4 in. * 3 in. = 60 in.

• 60 will become 60 in 3 .

Calculator, Practice Problems, and Answers

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• ↑ http://www.softschools.com/math/geometry/topics/volume_of_a_rectangular_prism/
• ↑ https://www.khanacademy.org/math/cc-fifth-grade-math/5th-volume/volume-word-problems/a/volume-of-rectangular-prisms-review
• ↑ https://www.omnicalculator.com/math/rectangular-prism-volume
• ↑ http://lrd.kangan.edu.au/numbers/content/03_volume/03_page.htm
• ↑ https://sciencing.com/calculate-volume-rectangular-prism-2040920.html

About This Article

1. Find the length, width, and height of the rectangular prism. 2. Multiply the length, width, and height to get the volume. 3. Write the answer in cubic units. Did this summary help you? Yes No

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Volume of a Rectangular Prism – Definition with Examples

What is a rectangular prism.

• Difference between Rectangle & Rectangular Prism

The Formula for Volume of a Rectangular Prism

Solved examples, practice problems, frequently asked questions.

You see it in boxes as you grab a tissue or pop open your box of cereal. You see it in books as you remove your bookmarks to begin reading. You see it in laptops as you finish typing your latest assignment. 

Yes, we are talking about the rectangular prism.

A rectangular prism is a three-dimensional shape with six faces. All the faces (top, bottom, and lateral faces) of the prism are rectangular so that all the pairs of opposite faces are congruent. It is also known as a cuboid. In short, a rectangular prism has four rectangular faces and two parallel rectangular bases. 

How is a rectangular prism different from a rectangle? 

To begin with, why is it important to know the difference between different types of shapes? 

Every shape has distinct properties and these properties help to know quantities such as volume, surface area, etc. Remember, you would not know to not put a rectangle on top of a triangle if you don’t know how they are different. 

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Difference Between Rectangle & Rectangular Prism

Now that we know what rectangular prisms are, let’s look at how we can calculate its volume.

By multiplying the base area of a prism by its height, you will get the volume of a prism. That is to say, the volume of a prism = base area × height.

Since a rectangular prism’s base is a rectangle itself, the volume of a rectangular prism, by applying the formula given above, will be:

Volume of a rectangular prism (V) = l × w × h

“l” means the base length, and

“w” means the base width,

“h” means the height

Example 1: Find out the volume of a rectangular prism with base length 9 inches, base width 6 inches, and height 18 inches, respectively.

Length (l) = 9 inches

Width (b) = 6 inches

Height (h) = 18 inches

So, the volume of the given rectangular prism = l × w × h = 9 × 6 × 18 = 972 cubic inches.

Example 2: Find out the height of a rectangular prism whose base area is 20 sq. units and a volume is 60 cubic units.

Given is the base area of the rectangular prism = 20 sq. units

And the volume of the rectangular prism = 60 cubic units

Now, applying the volume of the rectangular prism formula, 

base area × height = 60 cubic units.

⇒ 20 × height = 60

⇒ height = 60 ÷ 20 units

⇒ height = 3 units 

Example 3: Find out the base area of a rectangular prism with the help of the given measurements: length = 12 inches, height = 20 inches, and volume = 2,160 cubic inches. 

Length (l) = 12 inches

Height (h) = 20 inches

Volume (V) = 2,160 cubic inches

The volume of the rectangular prism = l × w × h  

⇒ 2,160 = 12 × w × 20 

⇒ 2,160 ÷ (12 × 20) = w

⇒ 9 = w

Therefore, width (w) = 9 inches.

Area = l × w = 12 × 9 = 108 sq. inches.

The volume of a rectangular prism is an important concept for 5th graders to learn. As we have already discussed, the volume of a rectangular prism is the product of its dimensions, i.e., length, width, and height. This can be better understood with practical examples. Using SplashLearn, students can practice each example with online interactive worksheets. This game-based learning app makes learning fun and keeps your child engaged.

Every game on SplashLearn is curriculum-based and scientifically designed. To boost your kid’s knowledge in mathematics and allow them to practice mathematics fearlessly, you can sign up to SplashLearn for free!

Volume of Rectangular Prism

Attend this Quiz & Test your knowledge.

Choose the correct formula to determine the volume of a rectangular prism?

Find out the base area of a rectangular prism whose height is 7 inches and volume is 343 cubic inches., find out the volume of a rectangular prism whose base area is 35 cm and height is 10 cm..

What is another name for a rectangular prism?

A rectangular prism is also known as a cuboid.

Is the volume of a rectangular prism the same as a cuboid?

Yes, the volume of a rectangular prism is the same as the volume of a cuboid.

What is an oblique rectangular prism?

An oblique rectangular prism is a prism with six rectangular faces, but the lateral faces are not perpendicular to the bases.

What is the surface area of a rectangular prism?

The surface area of a rectangular prism is the sum of the area of each of its faces. It is given by the formula, 2(lw + wh + hl), where l is length, w is width, and h is the height of the rectangular prism.

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Volume of Prisms

Solid geometry is concerned with three-dimensional shapes. In these lessons, we will learn

• what is a prism?
• how to find the volume of prisms.
• how to solve word problems about prisms.

Related Pages Volume Formula Volume Of Prism Worksheet Volume Formulas Explained More Geometry Lessons

A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base.

The other faces are in the shape of parallelograms. They are called lateral faces.

A right prism is a prism that has its bases perpendicular to its lateral surfaces. If the bases are not perpendicular to its lateral bases then it is called an oblique prism.

When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.

What is a prism and distinguishes between a right prism and an oblique prism?

How to label the parts of a prism and how to distinguish between an oblique and a right prism?

Volume of a Prism

The volume of a right prism is given by the formula:

Volume = Area of base × height = Ah

where A is the area of the base and h is the height or length of the prism.

Worksheet to calculate volume of prisms and pyramids.

Example: Find the volume of the following right prism.

Solution: Volume = Ah = 25 cm 2 × 9 cm = 225 cm 3

Example: Find the volume of the following right prism

Solution: First, we need to calculate the area of the triangular base.

We would need to use Pythagorean theorem to calculate the height of the triangle.

h 2 + 3 2 = 5 2

Volume of prism = Ah = 12 cm 2 × 8 cm = 96 cm 3

How to find the volume of a rectangular and a triangular prism? Step 1: Find the area of the base. Step 2: Multiply the area of the base times the height.

How to find the volume of any prism, right or oblique using a general formula?

Word problems about volume of prisms

The following video shows how to solve a word problem involving the volume of prisms.

Example: Find the volume and capacity of a swimming pool which is made up of a rectangular and trapezoidal prism.

Use the given net to determine the surface area and volume of a triangular prism

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Rectangular Prism

A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent. Like all three-dimensional shapes, a rectangular prism also has volume and surface area. A rectangular prism is also known as a cuboid. Let us learn more about a rectangular prism along with the formulas to find its volume and surface area.

What is a Rectangular Prism?

A rectangular prism is a prism whose bases (the top face and the bottom face) are also rectangles . It has 6 faces in all, out of which there are 3 pairs of identical opposite faces, i.e., all the opposite faces are identical in a rectangular prism. It has three dimensions, length, width, and height. Some examples of a rectangular prism in real life are rectangular tissue boxes, school notebooks, laptops, fish tanks, large structures such as cargo containers, rooms, storage sheds, etc. The following figure shows a rectangular prism and its net, which is a two-dimensional representation of the prism when its faces are opened on a 2D plane.

Faces Edges Vertices of a Rectangular Prism

A rectangular prism has 6 faces, 12 edges (sides) and 8 vertices (corners). In the 12 edges, 3 edges intersect to form right angles at each vertex.

Types of Rectangular Prisms

There are two types of rectangular prisms that are classified depending on the shape of the faces or the angle made by the faces with the base.

• Right rectangular prism: In a right rectangular prism, the faces are perpendicular to each of its bases. In this, all side faces are rectangles.
• Oblique rectangular prism: In an oblique rectangular prism, the faces are not perpendicular to the bases. In other words, the faces in this prism are parallelograms .

In general, a rectangular prism without any specifications is a right rectangular prism.

Properties of Rectangular Prism

The properties of a rectangular prism are given below which help us to identify it easily.

• A rectangular prism has 6 faces, 8 vertices, and 12 edges.
• In a right rectangular prism, the faces are rectangles, whereas, in an oblique rectangular prism, the faces are parallelograms.
• It has 3 dimensions which are length, width, and height.
• The opposite faces of a rectangular prism are congruent .

Rectangular Prism Formulas

In this section, we will learn the formulas of the volume and surface area of a rectangular prism . For both of these, let us consider a rectangular prism of length 'l', width 'w', and height 'h'. Along these dimensions, let us assume that 'l' and 'w' are the dimensions of the base. Here are the formulas for the volume and surface area of a rectangular prism.

Let us see how to derive these formulas.

Volume of Rectangular Prism

The volume of a rectangular prism is the space that is inside it. We know that the volume of any prism is obtained by multiplying its base area by its height. Here,

• The base area of the rectangular prism = lw (using the area of a rectangle formula)
• The height of the rectangular prism = h

Thus, the volume of the rectangular prism, V = lw × h = lwh.

Surface Area of Rectangular Prism

There are two types of surface areas of a rectangular prism, one is the total surface area (TSA) and the other is the lateral surface area (LSA).

• The total surface area of a rectangular prism is the sum of the areas of all of its faces.
• The lateral surface area of a rectangular prism is the sum of the areas of all its side faces (excluding the bases).

We can calculate the areas of the side faces of a rectangular prism using its net.

The total surface area (TSA) of a rectangular prism

= The sum of areas of all faces

= lw + lw + wh + wh + hl + hl

= 2 (lw + wh + hl)

The lateral surface area (LSA) of a rectangular prism

= The sum of areas of side faces

= wh + wh + hl + hl

= 2 (wh + hl)

We will see the applications of these volume and surface area formulas of a rectangular prism in the section of Rectangular Prism Examples given below.

☛ Related Links

• Triangular Prism
• Square Prism
• Right Rectangular Prism
• Hexagonal Prism

Rectangular Prism Examples

Example 1: Joe has a chocolate box whose shape resembles a rectangular prism. Its length is 6 in, height is 2 in and width is 4 in. Find the volume of the box.

The dimensions of the given chocolate box are,

length, l = 6 in

width, w = 4 in

height, h = 2 in

Its volume is, V = lwh

= 6 × 4 × 2

Answer: The volume of the box = 48 in 3 .

Example 2: A gift is packed in a rectangular box (rectangular prism) of dimensions 15 in, 10 in, and 8 in and it needs to be wrapped with gift paper. How much gift paper is required to wrap the gift box?

The dimensions of the given gift box are,

length, l = 15 in

width, w = 10 in

height, h = 8 in

To find the amount of gift paper required, we need to find the total surface area of the box.

TSA of a rectangular prism = 2 (lw + wh + hl)

= 2 [(15 × 10) + (10 × 8) + (8 × 15)]

= 2 (150 + 80 + 120)

= 700 in 2 .

Answer: The amount (area) of the gift paper required = 700 in 2 .

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Practice Questions on Rectangular Prism

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FAQs on Rectangular Prism

A rectangular prism is a 3-d solid shape that has 6 rectangular faces in which all the pairs of opposite faces are congruent . It has 8 vertices, 6 faces, and 12 edges. A few real-life examples of a rectangular prism include rectangular fish tanks, shoe boxes, etc.

What is a Rectangular Prism also Known as?

A rectangular prism is also known as a cuboid . It resembles a cube, but it is not a cube. All its properties are the same as that of a cube except that its faces are rectangles, whereas the faces of a cube are squares.

What is the Difference Between a Cube and a Rectangular Prism (Cuboid)?

Both cube and cuboid are prisms. A cube has 6 faces which are identical squares whereas a rectangular prism has 6 faces in which all the faces are rectangles. The opposite faces in a rectangular prism are identical.

What is the Ratio of Corners to Faces in Rectangular Prisms?

A rectangular prism has 8 corners (vertices) and 6 faces. So the ratio of the corners to faces in a rectangular prism is 8 : 6 (or) 4 : 3.

Why is a Rectangular Prism Called a Polyhedron?

A polyhedron is a 3-d shape in which all the 6 faces are in the shape of a polygon, i.e., in a polyhedron, the top and bottom faces are congruent polygons and the remaining 4 faces are lateral faces that are parallelograms. Therefore, it is called a polyhedron.

What is the Volume of a Rectangular Prism?

The volume of a rectangular prism is the space inside the prism. It is calculated by multiplying its base area by its height. Thus, the formula for the volume of a rectangular prism is Volume (V) = lwh; where 'l' is the length, 'w' is the width, and 'h' is the height of the prism and its base area (area of the rectangle of length 'l' and width 'w') is lw.

What is the Total Surface Area of a Rectangular Prism?

The total surface area of a rectangular prism is obtained by adding the areas of all its faces. Thus, the total surface area (TSA) of a rectangular prism is TSA = 2 (lw + wh + hl); where 'l' is the length, 'w' is the width, and 'h' is the height of the prism.

What is the Lateral Surface Area of a Rectangular Prism?

The lateral surface area of a rectangular prism is the sum of the areas of all its faces excluding the bases. Thus, the lateral surface area (LSA) of a rectangular prism of length 'l', width 'w', and height 'h' is LSA = 2 (wh + hl).

What is the Net of a Rectangular Prism?

The net of a rectangular prism is a two-dimensional representation of the prism which shows the faces of the prism if they are laid out flat. The net of a triangular prism has 6 rectangles in which 2 rectangles are the bases and the other 4 rectangles are its lateral faces.

What is a Right Rectangular Prism?

A right rectangular prism is a three-dimensional (3D) solid shape which has 6 faces, 12 edges, and 8 vertices. It is commonly known as the cuboid. All the angles that are formed at the vertices of this prism are right angles.