Question

A rectangular prism has a volume of 448 cubic centimeters. The height is 7 centimeters and the length is equal to the width.
Question
What is the ,begin emphasis,width,end emphasis, of the rectangular prism? Enter the answer in the box.

Answer 1

To find the width of the rectangular prism, we can start with the formula for the volume of a rectangular prism:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

Given that the volume is 448 cubic centimeters, the height is 7 centimeters, and the length is equal to the width (let's denote both as \( x \)), we can set up the equation:

\[
448 = x \times x \times 7
\]

This simplifies to:

\[
448 = 7x^2
\]

Next, we can divide both sides by 7 to isolate \( x^2 \):

\[
\frac{448}{7} = x^2
\]

Calculating the left side:

\[
64 = x^2
\]

To find \( x \), we take the square root of both sides:

\[
x = \sqrt{64}
\]

This gives us:

\[
x = 8
\]

Since \( x \) represents both the length and the width, the width of the rectangular prism is:

\[
\boxed{8} \, \text{centimeters}
\]