Q15. - Algebra 1

Question

GEOMETRY The volume of the rectangular prism at the right is 440 cubic centimeters. What is the width?

Step-by-Step Solution

Answer

The width of the rectangular prism is 4 centimeters.

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.

The volume of the rectangular prism is 440 cubic centimeters.

 

It is clear from the figure that the length of the prism is 10 centimeters and the height of the prism is 11 centimeters.

Then, $l=10\mathrm{cm}$, $h=11\mathrm{cm}$.

 

Let the width of the prism be w.

Step 3. Calculate the width.

Put $l=10$, $h=11$ and $V=440$ in $V=whl$ to get,

$$\begin{gathered} 440=w\times 11\times 10 \\ 440=110w \\ w=\frac{440}{110} \\ w=4 \end{gathered}$$

So, $w=4$.

Step 4. Determine the unit.

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

 

So, the width of the rectangular prism is 4 centimeters.