Chapter 1.6, Problem 43PPS

(a)

To determine

To find: Fencing will she need.

Answer to Problem 43PPS

The length of the fence is equal to the perimeter of the square having the side $32ft,$ and is equal to $4\times 32=128ft$ .

Explanation of Solution

Given information:

Line 1: Circular swimming pool with diameter $=20feet.$

Calculation:

Consider that Ms Neus has a circular swimming pool that is $20$ feet in diameter.

The area of the circle having radius $r$ is $A=\pi r^2$ .

Here the radius is:

  $\begin{array}{c}r=\frac{d}{2}\\ =\frac{20}{2}\\ =10\end{array}$

Therefore, the area of the swimming pool is $A$ .

  $\begin{array}{c}A=\pi r^2\\ =\pi {(}^{10}\\ =314.16squarefeet.\end{array}$

The dimensions of the square fence around the pool so that the fence is a minimum of $6$ feet from any edge of the pool are $20+6+6=32ft$ by $32ft$ .

Therefore, the length of the fence is equal to the perimeter of the square having the side $32ft,$ and is equal to $4\times 32=128ft$ .

(b)

To determine

To find: The percent of the area enclosed by the fence is not occupied by the pool.

Answer to Problem 43PPS

The percent of the area enclosed by the fence is not occupied by the pool is $69.32$ .

Explanation of Solution

Given information:

Line1: Circular swimming pool with diameter $=20feet.$

Calculation:

The area of the total square having side $32ft$ is $S=x^2$

  $\begin{array}{c}S=x^2\\ ={(}^{32}\\ =1024sqft.\end{array}$

Therefore, the percentage of the area enclosed by the fence is not occupied by the pool is about

  $\frac{709.84}{1024}\times 100=\mathrm{69.32.}$