Finding the length and width of the swimming pool, using what is given.

Question

A swimming pool is in the shape of a rectangular prism. The pool is 8 feet deep. It’s length is 2 times it’s width. The volume of the pool is 21,904 cubic feet. Find the length and the width of the pool.

Answer 1

To begin to answer this question, you will want to determine the equation for the volume of a rectangular prism. In this case, the equation is length times width times height or:

V = l * w * h

In the question, you are given several pieces of information that you can then plug into the equation. For example, you know the volume is 21,904 ft³ because they tell you that directly. You also know that the pool is 8 feet deep. I consider the depth to be the same as the height. With that information, you now have the equation:

21,904 ft³ = l * w * (8ft)

You are also told that the length is 2 times the width. Written as an equation, you would say that

l = 2w

Now, you can substitute that 2w for l to get the equation:

21,904 ft³ = (2w) * w * 8ft

We know that when you multiply a variable times itself, you get a squared variable, so 2w * w = 2w² and that

21,904 ft³ = 2w² * 8ft

Now, you can solve the equation to find w. At this point, it is easiest to drop the units of feet on the numbers to do the math. As long as all your numbers are in the same units (i.e. feet), you are good to go. Start by dividing each side by 8 to get

2738 = 2w²

Then divide both sides by 2 to get

1369 = w²

Finally, for this portion, take the square root of 1369 to get

w = 37 feet.

But you're not done yet. You know the width, and you know that l = 2w. Plug the value for w (37) into this equation to get the length, which is 74 feet.

The final answer is that the width of the pool is 37 feet and the length is 74 feet.

You can check your answer by plugging the length, width, and height (depth) into the equation for volume to see if you get 21,904ft³.

If you take 8 ft x 37 ft x 74 ft, you get 21,904 ft³ and you know that you answer is correct.