Q13. - Algebra 1

Question

SWIMMING POOLS A children's rectangular pool holds 480 cubic feet of water. What is the depth of the pool if its length is 30 feet and its width is 16 feet?

Step-by-Step Solution

Answer

The depth of the pool is 1 foot.

Step 1. State the formula.

The formula of volume of a rectangular prism is $V=whl$, where V is the volume, w is the width, h is the height and l is the length of the prism.

Step 2. List the given data.

A children’s rectangular pool holds 480 cubic feet of water. This implies that the volume of the pool is 480 cubic feet.

 

It is also given that the length of the pool is 30 feet and its width is 16 feet.

Then, $l=30\mathrm{ft}$, $w=16\mathrm{ft}$.

 

Let the depth of the pool, or equivalently, the height is h.

Step 3. Calculate the depth.

The shape of a swimming pool is that of a rectangular prism.

 

Put $l=30$, $w=16$ and $V=480$ in $V=whl$ to get,

$$\begin{gathered} 480=16\times h\times 30 \\ 480=480h \\ 1=h \end{gathered}$$

So, $h=1$.

Step 4. Determine the unit

Since the units of length and width are given as feet and the unit of volume is given as cubic feet, the unit of height must be feet.

 

So, the depth of the pool is 1 foot.