# Volume of prisms and cylinders

A prism has the same shape all the way through. Its volume is the area of the cross-section times the length.

Maths (school) · Part 05: Angles and area · Card 7 of 8 · Last updated 2026-10-19

## Analogy

Like stacking identical slices of bread to make a loaf.

## Example

**Cylinder r = 3, h = 10**

Cross-section = pi x 3^2 = 9 x pi
Volume = 9 x pi x 10
= 90 x pi = 282.7 cubic units

## In practice

Water tanks and tins are prisms or cylinders, so volume tells you how much they hold.

## Practice

### Flashcards

- **What is the volume of a prism?** Area of the cross-section times the length.

### Interview questions

**A cylinder has radius 3 cm and height 10 cm. Find its volume.**

- Area of the circle end = pi x 3^2
- That is 9 x pi, about 28.3 cm^2
- Multiply by the height 10
- Volume is about 282.7 cm^3

## Questions people ask

### What is the formula for volume of a cylinder?

Volume = pi x r^2 x h. The first part, pi x r^2, is the area of the circular end. Multiply by the height to find the volume. A cylinder with radius 3 and height 10 has volume 90 x pi, which is about 282.7.

### Why are volumes in cubic units?

Volume counts how many unit cubes fit inside a solid, so you multiply three lengths. The units are cubed: cm^3 or m^3. A box 2 cm by 3 cm by 4 cm has a volume of 24 cm^3. Capacity uses the same idea.

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