Find the circumference of a circle whose area is 100π cm2.
Circumference of a circle
Circumference = 2 x π x radius
Use the area to find the radius:
Area of a circle
Area of a circle = πr2
Where r = radius of the circle.
Area = 100π cm²
100π = πr2
Get rid of π by dividing both sides by π
100 = r2
Express 10 as a square: 100 = 102
102 = r2
Since the powers are equal, the bases must be equal: 10 = r
Therefore, the radius is 10 cm.
Substitute the radius into the circumference formula:
Circumference = 2 x π x 10 cm
Circumference = 20π cm