Question

A community swimming pool is a rectangular prism that is 30 feet long, 12 feet wide, and 5 feet deep. The wading pool is half as long, half as deep, and the same width as the larger pool.

How many times greater is the volume of the swimming pool than the volume of the wading pool?

Enter your answer as a number, like this: 42
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Answer 1

The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.

Explanation:

By definition of rectangular prism, we get the respective formulas for the volumes of the community swimming pool and the wadling pool, respectively:

Community swimming pool

`V_(c) = l\cdot w\cdot h (1)`

Wading pool

`V_(w) = \left((1)/(2)\cdot l \right)\cdot \left((1)/(2)\cdot h\right)\cdot w (2)`

Where:

l – Length of the swimming pool, measured in feet.

h – Depth of the swimming pool, measured in feet.

w – Width of the swimming pool, measured in feet.

`V_(c)` – Volume of the community swimming pool, measured in cubic feet.

`V_(w)` – Volume of the wading swimming pool, measured in cubic feet.

The ratio of the volume of the community swimming pool to the volume of the wadling pool is:

`(V_(c))/(V_(w)) = (l\cdot w \cdot h)/(\left((1)/(2)\cdot l \right)\cdot \left((1)/(2)\cdot h\right)\cdot w) (3)`

`(V_(c))/(V_(w)) = (1)/((1)/(4) )`

`(V_(c))/(V_(w)) = 4`

The volume of the community swimming pool is 4 times greaters than the volume of the wading pool.