To determine how much cardboard Cherese will have left over after building the box, we first need to calculate the surface area of the box.
The formula for the surface area \(A\) of a rectangular prism (box) is given by:
\[ A = 2(lw + lh + wh) \]
where:
- \(l\) = length,
- \(w\) = width,
- \(h\) = height.
For Cherese's box:
- Length \(l = 10\) inches,
- Width \(w = 9\) inches,
- Height \(h = 7\) inches.
Now, we substitute the values into the formula:
\[ A = 2(10 \times 9 + 10 \times 7 + 9 \times 7) \]
Calculating each part:
- \(10 \times 9 = 90\)
- \(10 \times 7 = 70\)
- \(9 \times 7 = 63\)
Adding these values:
\[ 90 + 70 + 63 = 223 \]
Now, multiply by 2 for the total surface area:
\[ A = 2 \times 223 = 446 \text{ square inches} \]
Now, Cherese buys 500 square inches of cardboard. We find how much is left over by subtracting the surface area from the amount she purchased:
\[ \text{Leftover cardboard} = 500 - 446 = 54 \text{ square inches} \]
Thus, the answer is:
54 in. squared.