Chapter 9.3, Problem 32E

To determine

To Find: The length and width of the pond if the pond has a depth of 24 inches and a volume of 72000 cubic inches and the length of the pond is two times its width.

Answer to Problem 32E

The required length is 77.46 inches and the width is 38.73 inches.

Explanation of Solution

Given information:

The pond has a depth of 24 inches and a volume of 72000 cubic inches.

The length of the pond is two times its width.

Calculation:

The length l is two times the width w, so $l=2w$ .

Write an equation using the formula for the volume of a rectangular prism.

  $V=lwh$

(Write the formula)

  $72000=2w\left(w\right)\left(24\right)$

(Substitute 72000 for V, 2w for l, and 24 for h)

  $72000=48w^2$

(Multiply)

  $1500=w^2$

(Divide each side by 48)

  $\pm \sqrt{1500}=w$

(Take the square root of each side)

So, the solutions are $\sqrt{1500}$ and $-\sqrt{1500}$ . Use the positive solution.

Therefore the width is $\sqrt{1500}\approx 38.73$ inches and the length is $2\sqrt{1500}\approx 77.46$ inches.