Four different ways to find the radius of a circle

The four different ways to find the radius of a circle are shown below:

  • Using the diameter
  • Using the circumference
  • Using the area
  • Using the central angle of a sector and the area of the sector

How to find the radius of a circle using the diameter


In a circle, the radius is always half the length of its diameter.

r = d / 2

Example #1:

Find the radius if the diameter is 20 inches

r = d / 2 = 20 / 2 = 10

The radius is 10 inches.

How to find the radius of a circle using the circumference


The example below illustrates clearly how to find the radius of a circle when the circumference is known.

Example #2:

Suppose the circumference of a circle is 50.24 inches. Find the radius, r.

find the radius of a circle given circumference

The radius is 8 inches when the circumference is 50.24 inches

How to find the radius of a circle using the area


The formula to find the area of a circle is A = πr2

Example #3:

Find the radius if the area of the circle is equal to 50 cm2

A = πr2

Substitute 50 for A 

50 = πr2

Substitute 3.14 for π

50 = 3.14r2

Divide both sides of the equation by 3.14

50 ÷ 3.14 = (3.14 ÷ 3.14)r2

15.92 = (1)r2

15.92 = r2

r = √(15.92)

r = 3.98

The radius is 3.98 cm

How to find the radius of a circle using the central angle of a sector and the area of the sector

The formula to find the area of a sector is A = (n0 / 3600)πr2

n0 is the measure of the central angle 

Example #4:

Find the radius if the central angle is 90 degrees and the area of the sector is equal to 19.63 cm2

A = (n0 / 3600)πr2

Substitute 19.63 for A 

19.63 = (n0 / 3600)πr2

Substitute 90 degrees for n0 

19.63 = (900 / 3600)πr2

19.63 = (0.25)πr2

19.63 = 0.785r2

Divide both sides by 0.785

19.63 ÷ 0.785 = (0.785 ÷ 0.785)r2

25.0063 = (1)r2

25.0063 = r2

r = √(25.0063)

r = 5

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