---
title: "Volume: cheat sheet"
subtitle: "Area, volume, circles and Pythagoras"
---

# Volume

> The words and methods from this unit, with an example of each.

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**volume of a prism**: Each layer is the base (the cross-section); the height counts the layers. For a box, $V = l \times w \times h$.

$$V = A \times h$$

_A 4 by 3 by 5 box in layers of 12 cubes_

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:::keep-together

**cross-section**: The shape that is the same all the way along a prism, like a slice of bread. A triangular prism's cross-section is a triangle: halve first.

$$V = \tfrac{1}{2} \times 6 \times 4 \times 10 = 120 \text{ cm}^3$$

_A triangular prism, half of a 4 by 3 box, 5 layers high_

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**capacity**: How much a container holds. A 10 cm cube holds 1 litre.

$$1 \text{ cm}^3 = 1 \text{ mL} \qquad 1000 \text{ cm}^3 = 1 \text{ L}$$

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**volume and capacity**: A cubic metre is 100 × 100 × 100 = 1 000 000 cm³: convert each of the three lengths.

$$1\ \text{cm}^3 = 1\ \text{mL}, \quad 1000\ \text{cm}^3 = 1\ \text{L}, \quad 1\ \text{m}^3 = 1000\ \text{L}$$

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:::keep-together

**volume of a prism**: The area of the end times the length, for any right prism. Divide to find a missing length.

$$V = A h \qquad h = V \div A$$

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