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

# Circles

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

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**radius and diameter**: The radius goes from the centre to the edge; the diameter right across through the centre. A chord joins any two points; the diameter is the longest.

$$d = 2r \qquad r = d \div 2$$

_A circle with its centre, radius, diameter, a chord and the circumference_

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**pi**: The circumference divided by the diameter: the same for every circle. 3.14 and 22/7 are approximations.

$$\pi = \frac{C}{d} = 3.14159\ldots$$

_A circle rolled out flat: just over 3 diameters_

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**circumference**: Use the diameter, or double the radius. Backwards: $d = C \div \pi$. Exact answers keep π: $10\pi$ cm.

$$C = \pi d = 2\pi r$$

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**area of a circle**: Slices of a circle make a near-rectangle πr long and r high. The area is between 2r² and 4r². Do not mix it up with C = 2πr.

$$A = \pi r^2$$

_24 slices laid top to tail: nearly a rectangle πr by r_

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**radius from area**: Divide by π, then take the square root. A semicircle is half the area; its perimeter is half the circumference plus the diameter.

$$r = \sqrt{A \div \pi}$$

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