Question

Find the exact area of a circle having the given circumference.

4(
`√(3) \pi` )

A: 2
`√(3) \pi`
B: 4
`√(3) \pi`
C: 12
`\pi`

Answer 1

The answer is the option C

`12\pi\ units^(2)`

Explanation:

we know that

the circumference of a circle is equal to

`C=2\pi r`

In this problem we have

`C=4\pi√(3) \ units`

substitute in the equation and solve for r

`4\pi√(3)=2\pi r`

`2√(3)= r` ------->
`r=2√(3)\ units`

Find the area of the circle

Remember that

The area of a circle is equal to

`A=\pi r^(2)`

substitute the value of r

`A=\pi (2√(3))^(2)`

`A=12\pi\ units^(2)`