To find out how much cardboard Cherese will have left over, we first need to calculate the surface area of the box she wants to build.
The formula for the surface area \(A\) of a rectangular box (also known as a rectangular prism) is:
\[ A = 2(lw + lh + wh) \]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the box.
Given:
- Length \(l = 10\) inches
- Width \(w = 9\) inches
- Height \(h = 7\) inches
Now, we can plug in these values:
\[ A = 2(10 \times 9 + 10 \times 7 + 9 \times 7) \]
Now, calculate each term:
- \(10 \times 9 = 90\)
- \(10 \times 7 = 70\)
- \(9 \times 7 = 63\)
Now sum these terms:
\[ 90 + 70 + 63 = 223 \]
Now multiply by 2 to get the total surface area:
\[ A = 2 \times 223 = 446 \text{ square inches} \]
Cherese buys 500 square inches of cardboard. To find how much is left over, we subtract the surface area from the amount purchased:
\[ \text{Leftover} = 500 - 446 = 54 \text{ square inches} \]
So, the amount of cardboard left over is 54 square inches.
The final answer is:
54 in.²