Question

Kyle wants to wrap the box in wrapping paper.

A rectangular prism with a length of 18 inches, width of 6 inches, and height of 3 inches.
What is the minimum amount of paper needed to cover the entire box?
180 inches squared
324 inches squared
360 inches squared
648 inches squared

Answer 1

To find the minimum amount of wrapping paper needed to cover the box, we need to calculate the surface area of the rectangular prism. The formula for the surface area \( A \) of a rectangular prism with length \( l \), width \( w \), and height \( h \) is:

\[
A = 2(lw + lh + wh)
\]

Given the dimensions:
- Length \( l = 18 \) inches
- Width \( w = 6 \) inches
- Height \( h = 3 \) inches

We can substitute these values into the formula:

1. Calculate \( lw \):
\[
lw = 18 \times 6 = 108 \text{ square inches}
\]

2. Calculate \( lh \):
\[
lh = 18 \times 3 = 54 \text{ square inches}
\]

3. Calculate \( wh \):
\[
wh = 6 \times 3 = 18 \text{ square inches}
\]

Now, substitute these values into the surface area formula:

\[
A = 2(108 + 54 + 18)
\]

Calculate the sum inside the parentheses:

\[
108 + 54 + 18 = 180
\]

Now calculate the surface area:

\[
A = 2 \times 180 = 360 \text{ square inches}
\]

Thus, the minimum amount of paper needed to cover the entire box is:

\[
\boxed{360} \text{ inches squared}
\]