Question

Find the circumference of a circle whose area is 60pi cm^2.

A.

`2 √(15\pi ) \: cm`
B.

`4 √(15\pi) \: cm`
C.

`30\pi \: cm`
D.

`900\pi \: cm`
​

Answer 1

none of the offered choices is correct

`circumference=4\pi√(15)\,\text{cm}`

Explanation:

We can use the area equation to find the radius of the circle, then use that to find the circumference.

A = πr²

60π = πr²

60 = r² . . . . . . . divide by π

√60 = 2√15 = r . . . . take the square root

Now, the circumference is given by ...

C = 2πr

C = 2π(2√15) = 4π√15 . . . . cm

_____

If the area were 60 cm², answer choice B would be correct. Since it is 60π cm², no answer choice is correct.