A circle with area $36 \pi$ is cut into quarters and three of the pieces are arranged as shown. What is the perimeter of the resulting figure?
(A) $6 \pi+12$
(B) $9 \pi+12$
(C) $9 \pi+18$
(D) $27 \pi+12$
(E) $27 \pi+24$

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-058.jpg?height=244&width=485&top_left_y=1298&top_left_x=1216)
A circle with area $36 \pi$ has radius 6 , since the the area of a circle with radius $r$ equals $\pi r^{2}$ and $\pi\left(6^{2}\right)=36 \pi$.

The circumference of a circle with radius 6 equals $2 \pi(6)=12 \pi$.

Therefore, each quarter-circle contributes $\frac{1}{4}(12 \pi)=3 \pi$ to the circumference.

The perimeter of the given figure consists of three quarter-circle sections and two radii from the circle.

Thus, its perimeter is $3(3 \pi)+2(6)=9 \pi+12$.

Answer: (B)