Chapter 12.5, Problem 41STP

To determine

To find the width of the deck.

Answer to Problem 41STP

The width of the deck is $\text{2 feet}$ .

Explanation of Solution

Given information:

The given statement is:

“A circular swimming pool with a diameter of $\text{28 feet}$ has a deck of uniform width built around it. If the area of the deck is $\text{60π square feet}$ , find its width.”

Calculation :

The result can be obtained by:

  $\begin{array}{l}\text{Area of the pool}=\text{π}{\left(14\right)}^2\left[\text{Diameter of pool}=\text{28ft, radius}=\text{14ft}\right]\\ \text{Area of the pool}=196\text{π}\\ \text{The area of the pool and deck combined}=196\text{π}+60\text{π}=256\text{π}\\ \text{Radius of pool and deck combined}\\ \Rightarrow {\text{πr}}^2\text{=}256\text{π}\\ \Rightarrow \text{r}=\sqrt{256}\\ \Rightarrow \text{r}=16\text{ feet}\\ \text{The width of the deck}=16\text{ feet}-\text{14 feet}=\text{2 feet}\end{array}$

Hence, the width of the deck is $\text{2 feet}$ .