Question

A fountain is made up of two semicircles and a quarter circle. Find the perimeter of the fountain. Round to the nearest foot.14 ft14 ftThe perimeter of the fountain is about feet.

Answer 1

$\frac{35}{2}\pi\approx54.97\approx55ft$

1) Note that this fountain is made up of 2 semicircles, and 1 quarter circle. Note also that the diameter of those semicircles is 14 ft then the radius is 7

The perimeter can be found this way:

$\begin{gathered} 2\:semicircles=\frac{2\pi r}{2}+\frac{2\pi r}{2}=2\pi r\Rightarrow C=2\pi(7)\Rightarrow C=14\pi \\ 1\:quarter\:=\frac{2\pi r}{4}=\frac{\pi r}{2}\Rightarrow\frac{7\pi}{2} \\ \\ \end{gathered}$

2) Now, let's add them up:

$14\pi+\frac{7\pi}{2}=\frac{35}{2}\pi$

Thus this is approximately 55 ft