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# Volume of a prism
- URL: https://www.esheets.io/volume-of-a-prism/
- Published: 2026-08-07T16:50:22.000Z
- Updated: 2026-08-07T16:50:22.000Z
- Author: Richard Linnington
- Tags: Maths, Geometry and Shape

A prism is a 3D shape that has the same cross-section all the way through.

You can find the volume of any prism by calculating the area of its cross-section, then multiplying it by its length.

This worksheet provides practice on common prisms, including rectangular, triangular and trapezoidal prisms, as well as cylinders. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

This interactive worksheet generates eight questions to help you practise calculating the volume of various prisms.

The progression starts with a simple given cross-section and builds up to cylinders and a reverse problem where you must find a missing length.

#### What you’ll practise

- use volume = cross-sectional area × length
- calculate triangular and trapezoidal cross-sectional areas
- calculate volumes of compound prisms
- calculate cylinder volumes using πr²h

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

## Volume of a prism

Give all answers to 1 decimal place. For cylinders, use the π button or π = 3.142.

## Topic guide

### What is a prism?

A prism is a solid 3D shape that has a constant cross-section. This means that if you slice through it parallel to its front face, the shape you see remains exactly the same all the way through.

### Key method

To find the volume of any prism, use the formula:

**Volume = area of cross-section × length**

### Finding the cross-sectional area

Depending on the shape of the prism, you must calculate the area of the cross-section first:

- **Rectangle**: width × height
- **Triangle**: ½ × base × perpendicular height
- **Trapezium**: ½(a + b) × perpendicular height
- **Compound shape**: split into simple rectangles, find their individual areas, and add them together

### Cylinders

A cylinder is a prism with a circular cross-section. Since the area of a circle is πr², the formula for the volume of a cylinder is:

**V = πr²h**

If you are given the diameter of the cylinder, make sure you divide it by 2 to find the radius before substituting it into the formula.

### Worked example

**Question:** Calculate the volume of a triangular prism with a right-angled triangular cross-section. The triangle has a base of 6 cm and a height of 4 cm. The prism has a length of 10 cm.

**Step 1: Find the area of the cross-section.**  
Area of triangle = ½ × base × height  
\= ½ × 6 × 4  
\= 12 cm²

**Step 2: Multiply by the length of the prism.**  
Volume = 12 × 10  
\= 120 cm³

### Common mistakes

- Forgetting the ½ when calculating the area of a triangular cross-section.
- Using the diameter instead of the radius in the πr² formula.
- Multiplying all the given numbers together without first identifying the correct cross-section.
- Writing cm² instead of cm³ for the final volume.
- Rounding π or intermediate values too early, which makes the final answer inaccurate. (On this worksheet, answers should be rounded to 1 decimal place at the very end).