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?

Answer 1

To find the minimum amount of wrapping paper needed to cover the entire box, we need to calculate the surface area of the rectangular prism.

The formula for the surface area \( S \) of a rectangular prism is given by:

\[
S = 2lw + 2lh + 2wh
\]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

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

Let's calculate each part:

1. Calculate \( 2lw \):
\[
2lw = 2 \times 18 \times 6 = 216 \text{ square inches}
\]

2. Calculate \( 2lh \):
\[
2lh = 2 \times 18 \times 3 = 108 \text{ square inches}
\]

3. Calculate \( 2wh \):
\[
2wh = 2 \times 6 \times 3 = 36 \text{ square inches}
\]

Now, we add these areas together to find the total surface area:

\[
S = 216 + 108 + 36 = 360 \text{ square inches}
\]

Thus, the minimum amount of wrapping paper needed to cover the entire box is \( \boxed{360} \) square inches.