Question

Jackie is wrapping a birthday present. The gift box is in the shape of a rectangular prism. It has a length of 8 inches, a width of 10 inches, and a height of 3 inches. What is the minimum amount of wrapping paper she will need to completely cover the box?

Answer 1

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

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

Given the dimensions:
- Length \( l = 8 \) inches
- Width \( w = 10 \) inches
- Height \( h = 3 \) inches

Let's calculate the area of each pair of opposite faces:

1. The area of the top and bottom faces (length × width):
\[
lw = 8 \times 10 = 80 \text{ square inches}
\]
Since there are two such faces, their contribution to the surface area is:
\[
2(lw) = 2 \times 80 = 160 \text{ square inches}
\]

2. The area of the front and back faces (length × height):
\[
lh = 8 \times 3 = 24 \text{ square inches}
\]
Since there are two such faces, their contribution to the surface area is:
\[
2(lh) = 2 \times 24 = 48 \text{ square inches}
\]

3. The area of the left and right faces (width × height):
\[
wh = 10 \times 3 = 30 \text{ square inches}
\]
Since there are two such faces, their contribution to the surface area is:
\[
2(wh) = 2 \times 30 = 60 \text{ square inches}
\]

Now, we can sum all these contributions to find the total surface area:

\[
A = 160 + 48 + 60 = 268 \text{ square inches}
\]

Thus, the minimum amount of wrapping paper Jackie will need to completely cover the box is:

\[
\boxed{268} \text{ square inches}
\]