Track / Stage 2 / 158 of 240 #398 of 2444

Problem 398

Geometry Difficulty 2.6 Multiple choice CEMC Cayley · Canada · 2014

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?

Pick one

Official solution

A circle with area $36\pi$ has radius $6$ , since the the area of a circle with radius $r$ equals $\pi r^2$ and $\pi (6^2)=36\pi$ .

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 $3(3\pi)+2(6)=9\pi+12$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.