In Geometry and Measure study, you’ll likely encounter content on the volume of prisms.

At KS3 and GCSE Maths level particularly, you’ll be required to make calculations with various shapes using the relevant formulae.

### Volume of Prisms – Getting Started

The volume of a shape is the measure of the three-dimensional space it covers. The units of measurement for volume are cubic units, for example, cm³ or m³.

A prism is a solid (3D) object which is the same shape all the way through; it has a constant cross-section. To calculate the volume of a prism, including a circular prism, learn this formula by heart:

For example, the cross-section of this cuboid is a rectangle.

To calculate the area of the cross-section, it would be length × width. You would then multiply this by the height, hence the formula: length × width × height.

**Beyond Maths – Volume of Prisms KS3 Walkthrough Worksheet**

### Example Walkthroughs

**Example 1 **

Calculate the volume of the prism shown below.

The first step is to calculate the area of the cross-section. In other words, you need to calculate the area of the base of the shape. (The base is always the face which is the same as the crosssection).

This shape is a triangular prism; its base is a triangle. Therefore, you need to calculate the area of the triangle. Remember that the formula for calculating the area of a triangle is ½ × base × height.

- ½ × 5 × 4 = 10cm².

Now that you have the area of the cross-section, multiply it by its length to calculate the volume.

- 10 × 12 = 120cm³ (Don’t forget the units!)

**Example 2**

Calculate the volume of the cylinder, giving your answer correct to the nearest whole number.

Start by calculating the area of the cross-section. In other words – the area of the circle. Remember that the formula for calculating the area of a circle is πr².

- π × 42
- π × 16 = 50.26548246…cm²

(It’s important that you don’t round your answer at this stage – you could also leave your answer in terms of π, e.g. 16π.)

Now, multiply the area of the circle by the height.

- 50.26548246… × 8 = 402.1238597…

As you don’t have any further calculations to do, you should now round the answer to the degree to which the question has asked for. In this case, the nearest **whole **number.

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