Circles: cheat sheet

Area, volume, circles and Pythagoras · The words and methods from the lessons, with an example of each.

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

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

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

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

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}