Volume of a Prism – GCSE Maths Boost

How to calculate the volume of a prism

The volume of a prism is the amount of space inside it. Volume is measured in cubic units, such as ${cm}^{3}$ , $m^{3}$ or ${mm}^{3}$ .

1. Learn the formula

$Volume = Cross-sectional area \times Length$ A prism has the same cross-sectional shape all the way along its length.
For example, a triangular prism has a triangle at each end, while a rectangular prism has a rectangle at each end.

2. Example: a triangular prism

Volume of a Prism - GCSE Maths Revision Guide - Tutor In

A triangular prism with a triangular cross-section and a length of 10 cm.
Suppose the triangle at the end has:

Base = 6 cm
Height = 4 cm
Prism length = 10 cm

Step 1: Calculate the area of the triangular end.
The formula for the area of a triangle is:

$Area = \frac{1}{2} \times base \times height$ Substitute the numbers:

$Area = \frac{1}{2} \times 6 \times 4 = 12 {cm}^{2}$

Step 2: Multiply by the length of the prism.

$Volume = 12 \times 10$

$Volume = 120 {cm}^{3}$ Remember: calculate the area of the end shape first, then multiply it by the prism’s length.

3. Other prism formulas

Cross-sectional shape	Area of the end	Volume
Rectangle	$length \times width$	$l \times w \times L$
Triangle	$\frac{1}{2} \times b \times h$	$\frac{1}{2} b h \times L$
Trapezium	$\frac{1}{2} (a + b) \times h$	$\frac{1}{2} (a + b) h \times L$

Here, $L$ is the length of the prism.
Exam tip: Always write the final answer in cubic units, such as ${cm}^{3}$ , because volume measures three-dimensional space.

Volume of a Prism

1 / 10

The diagram shows a water container.
The container is 2/3 full with water.
The water is going to be used to fill cups. Each cup holds 175ml of water.
How many cups of water can be completely filled with water from the container?

2 / 10

The total surface area of a cube is 150cm².
What is the volume of the cube?
cm³

3 / 10

The diagram shows an empty water container.
The container is going to be filled using a hose pipe.
The water will flow into the container at a rate of 2 litres per second.
How long will it take for the container to be filled completely?
seconds

4 / 10

Here is a cube.
What is the volume of five of these cubes?
cm³

5 / 10

The diagram shows an empty water container.
Fiona is going to use a bucket to fill the container.
Each bucket can hold 12 litres of water.
How many buckets of water will be needed to fill the container?

6 / 10

The diagram shows a cuboid.
The volume of the cuboid is 120cm³.
What is the value of x?

7 / 10

Bob has a van. He is using the van to deliver boxes.
Each box is a cuboid, 60cm by 30cm by 40cm.
The van has the space for the bozes in the shape of a cuboid with: length 3m, width 1.8m, height 2m.
How many boxes can Bob fit into the van?

8 / 10

The diagram shows a cuboid ABCDEFGH.
ABCD is a square with an area of 25cm².
CG = 12cm.
What is the volume of the cuboid?
cm³.

9 / 10

The diagram shows a prism.
The cross-section of the prism is a trapezium.
What is the volume of the prism?
cm³

10 / 10

The diagram shows a prism.
What is the volume of the prism?
cm³

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