19.2 Circumference and area of circles — Learn

Prerequisites: calculate with fractions and decimals; recognise radius and diameter.

Objectives: calculate circumference and area from a radius or diameter, including exact answers in terms of $\pi$.

Circle measures

The radius runs from the centre to the circumference. The diameter crosses the centre, so $d=2r$. Circumference is the distance around a circle: $C=\pi d=2\pi r$. Area is $A=\pi r^2$.

Example 1. A circle has diameter 14 cm. Work out its circumference exactly.

Use $C=\pi d$: $C=\pi\times14$.

So $C=14\pi\text{ cm}$.

Example 2. A circular pond has radius 5 m. Work out its area, then estimate using $\pi=3.14$.

Use the radius in $A=\pi r^2$: $A=\pi\times5^2$.

So $A=25\pi\text{ m}^2$, approximately $78.5\text{ m}^2$ when $\pi\approx3.14$.

Watch out. Squaring the diameter gives the wrong area. Find the radius first, then square it.

Investigate how radius changes circle measures

Predict: if the radius doubles, predict what happens to circumference and area.

Explain: compare the two readouts. Why does area change by a different factor from circumference?

Progress check

The pond has radius $4$ m. Work out its exact circumference and its exact area. Then estimate each value using $\pi=3.14$.

You should now be able to

• find the radius from the diameter and the diameter from the radius;
• calculate circumference using $C=\pi d$ or $C=2\pi r$;
• calculate area using $A=\pi r^2$;
• give exact answers in terms of $\pi$ or use a stated approximation.