Area of a circle

Warm-up

Three quick questions from earlier lessons.

Discover

Cut a circle of radius $r$ into thin wedges and line them up: they form almost a rectangle, half the circumference long and $r$ tall. What is its area?

$\pi r \cdot r = \pi r^2$
$2\pi r$

Key idea

Area counts square units inside.

The area of a circle is

A = \pi r^2

(square units). The circumference

C = 2\pi r

is a length (units). If you know the diameter, halve it first.

Worked example

A pizza with diameter 12 in.

r = 6

Halve.

A = 36\pi \approx 113

in²

πr².

Your turn, guided

Your turn: the area of a circle with radius 10 (in terms of π, type pi).

100\pi

π · 100.

Practice ★

Find the area of a circle with radius 3 cm (exact, in terms of π).Not to scale
Find the area of a circle with radius 12 cm (exact, in terms of π).Not to scale

Find the area of a half-circle with radius 14 m (exact, in terms of π).Not to scale

Watch out!

Practice ★★

A round table has a diameter of 6 ft. Find its area (exact, in terms of π).Not to scale
A round table has a diameter of 9 ft. Find its area (exact, in terms of π).Not to scale

Boss problem. A round garden has a diameter of 18 m. Give exact answers in terms of π.

Exit ticket

Three questions to check you have got it.

Find the area of a circle with radius 3 cm (exact, in terms of π).Not to scale
Find the area of a circle with radius 12 cm (exact, in terms of π).Not to scale
Find the area of a circle with radius 7 cm (exact, in terms of π).Not to scale

Summary card

Area of a circle

$A = \pi r^2$ ; around is $C = 2\pi r$ .

Watch out: square the radius, not the diameter.

About this lesson