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Perimeter

# Circles: calculate circumference, radius, and diameter

 The diameter of a circle is 10 millimetres. What is the circle's radius?

Use this formula to relate the radius and the diameter.

d = 2 x r

The diameter is equal to 10 millimetres. Replace d by 10 in the formula.

 d = 2 × r 10 = 2 × r 10 ÷ 2 = r 5 = r

The circumference of a circle is the distance around the outside, just as the perimeter of a polygon is the distance around the outside. The circumference of a circle can be found by measuring its radius or diameter and the using the formula:

C = 2 × π × r     (or C = π × d)

 The radius of a circle is 2 centimetres. What is the circle's circumference?

Use 3.14 for π.

Use this formula to find the circumference from the radius.

C = 2 × π × r

Use 3.14 as an approximation for π.

π ≈ 3.14

The radius is 2 centimetre. Replace r by 2 in the formula.

 C = 2 × π × r ≈ 2 × 3.14 ×2 ≈ 12.56

The circumference is about 12.56 centimetres.

 The diameter of a circle is 8 metres. What is the circle's circumference?

Use 3.14 for π.

Use this formula to find the circumference from the diameter.

C = π × d

Use 3.14 as an approximation for π.

π ≈ 3.14

The diameter is 8 metres. Replace d by 8 in the formula.

 C = π × d ≈ 3.14 ×8 ≈ 25.12

The circumference is about 25.12 metres.

 The circumference of a circle is 12.56 metres. What is the circle's diameter?

Use 3.14 for π.

Use this formula to relate the diameter and the circumference.

C = π × d

Use 3.14 as an approximation for π.

π ≈ 3.14

The circumference is 12.56 metres. Replace C by 12.56 in the formula.

 C = π × d 12.56 ≈ 3.14 × d 12.56 ÷ 3.14 ≈ d 4 ≈ d

The diameter is about 4 metres.