To find out how much cardboard Cherese will have left over after building her box, we first need to calculate the surface area of the box.
The formula for the surface area \( A \) of a rectangular box is: \[ A = 2lw + 2lh + 2wh \] where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
For Cherese’s box:
- Length (\( l \)) = 10 inches
- Width (\( w \)) = 9 inches
- Height (\( h \)) = 7 inches
Now, we can plug in the values: \[ A = 2(10)(9) + 2(10)(7) + 2(9)(7) \]
Calculating each term:
- \( 2(10)(9) = 180 \)
- \( 2(10)(7) = 140 \)
- \( 2(9)(7) = 126 \)
Now, adding these results together: \[ A = 180 + 140 + 126 = 446 \text{ square inches} \]
Now that we know the surface area of the box is 446 square inches, we can find out how much cardboard Cherese will have left over after buying 500 square inches.
To find the leftover cardboard: \[ \text{Leftover Cardboard} = \text{Total Cardboard} - \text{Surface Area} \] \[ \text{Leftover Cardboard} = 500 - 446 = 54 \text{ square inches} \]
Thus, the amount of leftover cardboard is: \[ \boxed{54 \text{ in}^2} \]
The correct answer is B) 54 in².