Question

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

Answer 1

Answer:

The answer is the option C

$12\pi\ units^{2}$

Step-by-step explanation:

we know that

the circumference of a circle is equal to

$C=2\pi r$

In this problem we have

$C=4\pi\sqrt{3} \ units$

substitute in the equation and solve for r

$4\pi\sqrt{3}=2\pi r$

$2\sqrt{3}= r$ -------> $r=2\sqrt{3}\ units$

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

$A=\pi (2\sqrt{3})^{2}$

$A=12\pi\ units^{2}$

Answer 2

Circumference is given by
$C=2\pi r$
Area is given by
$A=\pi r^2$

figure out the radius of the circle, then use it to find area