Question

Cheryl needs to buy some cardboard to build a box 10 inches long, 9 inches wide, and 7 inches high. If she purchases 500 square inches of cardboard, how much will be left over?

(Hint: You must first calculate the surface area of the box. Then, calculate the amount that will remain from the 500 square inches of cardboard)

Surface Area of a Rectangular Prism: 2lw + 2lh + 2wh (1 point)
Responses

406 inches squared
406 inches squared

54 inches squared
54 inches squared

446 inches squared
446 inches squared

426 inches squared
426 inches squared

Answer 1

To calculate the surface area of the box, we will use the formula for the surface area of a rectangular prism:

\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]

where:
- \( l = 10 \) inches (length),
- \( w = 9 \) inches (width),
- \( h = 7 \) inches (height).

Now we will calculate each part:

1. \( 2lw = 2 \times 10 \times 9 = 180 \) square inches
2. \( 2lh = 2 \times 10 \times 7 = 140 \) square inches
3. \( 2wh = 2 \times 9 \times 7 = 126 \) square inches

Now, let's sum these areas to find the total surface area:

\[
\text{Surface Area} = 180 + 140 + 126 = 446 \text{ square inches}
\]

Cheryl buys 500 square inches of cardboard. To find out how much cardboard will be left over, we subtract the surface area of the box from the amount of cardboard purchased:

\[
\text{Leftover Cardboard} = 500 - 446 = 54 \text{ square inches}
\]

So the amount of cardboard that will be left over is **54 inches squared**.

The correct response is:
**54 inches squared**