Measure with the radius

The idea

The circumference of a circle of diameter d is πd, which is 2πr where r is the radius.

Half a diameter

We know C ÷ D = π, so the circumference is C = π × D. Now measure the circumference with the radius r instead. A radius is half of a diameter.

About how many radii fit into the circumference of a circle?

• 3 radii and a bit more
• 6 radii and a bit more
• 12 radii and a bit more

Radius sticks

Roll the wheel once for each size. This time the sticks are radii. See how the circumference is built from d = 2r.

Two ways to say it

The circumference of a circle of diameter d is πd. Since d = 2r, it is also 2πr, where r is the radius.

Every wheel rolled out 6 radii and a bit more, which is 2π ≈ 6.28 radii. The diameter d is 2r, so π × d = π × 2r = 2πr.

Notes

The circumference of a circle of diameter d is πd = 2πr, where r is the radius.

Check yourself

A circle has radius 7 cm. Use π ≈ 22/7. What is its circumference?

Answer: 44 cm

C = 2 × 22/7 × 7 = 2 × 22 = 44 cm.

A circle has diameter 10 m. Use π = 3.14. What is its circumference?

Answer: 31.4 m

C = π × d = 3.14 × 10 = 31.4 m.

Which expression is the same as πd?

A circular pond has circumference 62.8 m. Use π = 3.14. What is its radius?

Answer: 10 m

r = 62.8 ÷ (2 × 3.14) = 62.8 ÷ 6.28 = 10 m.

• 2πr — correct. Yes. d = 2r, so πd = π × 2r = 2πr.
• πr. πr is only half of 2πr.
• π + r. π and r are multiplied, not added.