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.

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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