Chapter 12.4, Problem 36PPS

To determine

To find:

The volume of water it takes to fill the pool.

Answer to Problem 36PPS

The volume of water it takes to fill the pool is $1575{\text{ ft}}^3$ .

Explanation of Solution

Given information:

The base of a reactangular swimming pool is sloped so one end of the pool is $6$ feet deep and the other end is $3$ feet deep also the width is $15$ width.

Calculation:

The swimming pool is a combination of a rectangular prism and a trapezoidal prism.

The base of the rectangular prism is $6\text{ ft}$ by $\text{10 ft}$ and the height is $\text{15 ft}$ .

The bases of the trapezoidal prism are $6\text{ ft}$ and $\text{3 ft}$ long and the height of the trapezoidal prism is $\text{15 ft}$ .

Total volume is:

  $\begin{array}{c}V=lwh+\left[\frac{1}{2}\left(b_1+b_2\right)h\right]h\\ =6\left(10\right)\left(15\right)+\left[\frac{1}{2}\left(6+3\right)10\right]15\\ =900+675\\ =1575{\text{ ft}}^3\end{array}$

Hence the volume of water it takes to fill the pool is $1575{\text{ ft}}^3$ .