Area of circles, sectors and composite figures

The area of a circle, semicircle, quadrant and sector, and the area of composite shapes involving circles.

Area of a circle

$$A = \pi r^2$$

Area of a sector

$$A = \frac{\theta}{360} \times \pi r^2$$

Area grows with the square of the radius

Double the radius and the area becomes four times as big.

Example 1●

Find the area of a circle with diameter $10$ cm, to 1 decimal place.

$r = 5$, so $A = \pi \times 25 \approx 78.5$ cm².

Example 2●●

A $20$ cm square has a circle of diameter $20$ cm cut from it. Find the area left, to 1 decimal place.

$400 - \pi \times 10^2 = 400 - 314.16$

$\approx 85.8$ cm²

Flashcards

Area of a circle

$\pi r^2$

Area of a semicircle

$\tfrac{1}{2}\pi r^2$

Exact area, r = 3

$9\pi$

Practice