What is the area of a circle with the circumference of 18 pi?

Answer 1

Circumference of any circle is:

C = (pi)/d

where

C is circumference

d is diameter

.

Area of any circle:

A = (pi)r^2

where

A is area

r is radius

.

Of course, radius is half the diameter or

r = d/2

Pulling it all together:

Since they gave you circumference, use the circumference formula to find d (diameter):

C = (pi)/d

18(pi) = (pi)/d

18=d

.

Extract radius (r):

r = d/2

r = 18/2

r = 9 cm

.

plug it into the formula for area of a circle:

A = (pi)r^2

A = (pi)9^2

A = 81(pi) square cm (this is what they're looking for)

OR

Circumference = 2piR = 18pi

R = 9

Area = piR^2 = 81pi