Circumference of a circle

About this lesson

Grade 7 › Measuring circles

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Circumference of a circle

Discover

Wrap a string around a can and compare it with the can's diameter. About how many diameters long is the string?

  1. A bit more than 3
  2. Exactly 2

Key idea

Circumference is about 3.14 diameters.

For every circle, circumferencediameter=π≈3.14\dfrac{\text{circumference}}{\text{diameter}} = \pi \approx 3.14. So C=πd=2πrC = \pi d = 2\pi r, where the diameter dd is twice the radius rr.

Worked example

A bike wheel of radius 13 in.

d=26d = 26 in
d = 2r.
C=26π≈81.7C = 26\pi \approx 81.7 in
C = πd.

Your turn, guided

Your turn: circumference 18π18\pi. The diameter.

1818
C = πd.

Practice ★

  1. A circle has a diameter of 26 cm. Find its circumference (exact, in terms of π).Not to scale
  2. A circle has a diameter of 24 cm. Find its circumference (exact, in terms of π).Not to scale
  1. A wheel has a radius of 16 in. How far does it roll in one full turn (exact, in terms of π)?Not to scale

Watch out!

Practice ★★

  1. A circle has a circumference of 26π26\pi cm. Find its radius (cm).
  2. A circle has a circumference of 33π33\pi cm. Find its radius (cm).

Exit ticket

Three questions to check you have got it.

  1. A circle has a diameter of 26 cm. Find its circumference (exact, in terms of π).Not to scale
  2. A circle has a diameter of 24 cm. Find its circumference (exact, in terms of π).Not to scale
  3. A circle has a diameter of 11 cm. Find its circumference (exact, in terms of π).Not to scale

Summary card

Circumference

C=πd=2πrC = \pi d = 2\pi r.

Watch out: radius or diameter? Check before using π.

End of the lesson

Next lesson: Area of a circle Back to the chapter

Answers: Circumference of a circle

A

  1. 26π26 \pi
  2. 24π24 \pi

B

  1. 32π32 \pi

C

  1. 1313
  2. 332\frac{33}{2}

D

  1. 26π26 \pi
  2. 24π24 \pi
  3. 11π11 \pi

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