Chapter A.2, Problem 50AYU

To determine

To find: What is the area of the deck? How much fence is required to enclose the deck?

Answer to Problem 50AYU

$129\pi$; $6\pi$

Explanation of Solution

Given:

A circular swimming pool that is 20 feet in diameter is enclosed by a wooden deck that is 3 feet wide.

Formula Used:

Area of the circle $=\pi r^2$ and Circumference of the circle $=2\pi r$.

Calculation:

Area of the swimming pool $=\pi r^2=\pi \times {20}^2=400\pi$.

Area of the swimming pool with deck $=\pi r^2=\pi \times {23}^2=529\pi$.

The area of the deck $=529\pi -400\pi =129\pi$.

Circumference of the swimming pool $=2\pi r=2\pi \times 20=40\pi$.

Circumference of the swimming pool with deck $=2\pi r=2\pi \times 23=46\pi$.

The fence is required to enclose the deck $=46\pi -40\pi =6\pi$.