Parts of a circle

Years 6 to 11

The radius, diameter and circumference, and how they are linked.

A circle with the radius, diameter and circumference marked.

For learners

The radius goes from the centre of a circle to the edge. The diameter goes all the way across, through the centre. The diameter is twice the radius.

The circumference is the distance around the edge of the circle.

Measure the circumference and divide by the diameter, and you always get about 3.14. This number is called pi (π).

A worked example

A circle has a diameter of 10 cm. Find its circumference. Use π = 3.14.

$C = π \times d$ .
$3.14 \times 10 = 31.4$ .
The circumference is 31.4 cm.

For grown-ups

Circumference $C = π d = 2 π r$ and area $A = π r^{2}$ . Learners often mix up the two. Perimeter-type answers are in plain units; area answers are in square units.

Common mistakes

Using the diameter in the area formula where the radius is needed.
Mixing up $2 π r$ and $π r^{2}$ .
Forgetting the units are squared for area.

Why it matters

Wheels, clocks, pipes, planets and waves all involve circles.

Topics in quarter that use this

Parts of a circle
Circumference of a circle
Area of a circle
Arc length and sector area
Volume of a cylinder
Volume of cones and spheres
Radians