Question

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

Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? Round to the nearest tenth.

0.2 inches
4.5 inches
46.1 inches
414.7 inches

Answer 1

To find the width \( w \) of the rectangular prism, we can rearrange the volume formula \( V = lwh \) to solve for \( w \):

\[
w = \frac{V}{lh}
\]

We are given:
- Volume \( V = 138.24 \) cubic inches
- Height \( h = 9.6 \) inches
- Length \( l = 3.2 \) inches

Now, we can substitute the values into the formula:

\[
w = \frac{138.24}{3.2 \times 9.6}
\]

First, calculate \( 3.2 \times 9.6 \):

\[
3.2 \times 9.6 = 30.72
\]

Now, substitute this back into the formula for width \( w \):

\[
w = \frac{138.24}{30.72}
\]

Now perform the division:

\[
w \approx 4.5
\]

Therefore, the width of the rectangular prism is approximately **4.5 inches** when rounded to the nearest tenth. Thus, the correct answer is:

**4.5 inches**