10C

Pi and the circumference of a circle

Parts of a circle, the number pi, and the circumference formulas C = πd and C = 2πr, including perimeters of semicircles.

Parts of a circle

The radius $r$ goes from the centre to the edge. The diameter $d = 2r$ goes right across through the centre. The circumference $C$ is the distance around.

Pi

For every circle, $C \div d$ is the same number, called pi: $\pi = 3.14159\ldots$ It never ends and never repeats.

Circumference

$$C = \pi d = 2\pi r$$

Circumference grows in proportion to radius

Double the radius and the circumference doubles.

Example 1●

Find the circumference of a circle of radius $6$ cm, to 1 decimal place.

$C = 2 \times \pi \times 6 \approx 37.7$ cm

Example 2●●

Find the perimeter of a semicircle with diameter $10$ m, to 1 decimal place.

Curved part: $\tfrac{1}{2} \times \pi \times 10 \approx 15.71$ m.

Add the diameter: $15.71 + 10 \approx 25.7$ m.

Do not forget the straight edge.

Flashcards

Circumference formula

$C = \pi d$ or $C = 2\pi r$

Diameter in terms of radius

$d = 2r$

$pi$ to 2 d.p.

$3.14$

Practice

Find the circumference of a circle of radius $6$ cm (1 d.p.).
Find the perimeter of a semicircle with diameter $10$ m (1 d.p.).
Find the circumference of a circle with diameter $10$ cm (1 d.p.).
A circle has radius $7$. What is its diameter?
The exact circumference of a circle with radius $4$ is:
A circle has circumference $62.8$ cm. Find its radius, to the nearest whole number.
A bike wheel has diameter $60$ cm. How far does it roll in one turn (1 d.p.)?
Which is true for every circle?