Question

The town swimming pool is d feet deep. The width of the pool is 5 feet greater than 5 times its depth. The length of the pool is 50 feet greater than 5 times its depth. Enter a simplified expression to represent the volume of the pool.

Answer 1

`V = 25d ^ 3 + 275d ^ 2 + 250d`

Explanation:

If the pool has a rectangular shape then its volume can be written as:

V = Width * Length * Depth

Let's call:

w = width

l = length

d = depth.

So we know from the statement of the problem that:

`d = d`

`w = 5 + 5d` (5 feet more than 5 times the depth)

`l = 50 + 5d` (50 feet more than 5 times the depth)

Then, the volume can be written according to the depth as:

`V = d(5 + 5d)(50 + 5d)`

`V = d[250 + 25d + 250d + 25d ^ 2]`

`V = 25d ^ 3 + 275d ^ 2 + 250d`