To determine how much cardboard Cherese will have left over after building the box, we first need to find the surface area of the box.
The surface area \( S \) of a rectangular box can be calculated using the formula:
\[ S = 2(lw + lh + wh) \]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- Length (\( l \)) = 10 inches
- Width (\( w \)) = 9 inches
- Height (\( h \)) = 7 inches
Now we can plug the dimensions into the formula:
\[ S = 2(10 \cdot 9 + 10 \cdot 7 + 9 \cdot 7) \]
Calculating each term:
- \( 10 \cdot 9 = 90 \)
- \( 10 \cdot 7 = 70 \)
- \( 9 \cdot 7 = 63 \)
Now sum these: \[ 90 + 70 + 63 = 223 \]
Then multiply by 2: \[ S = 2 \cdot 223 = 446 \text{ square inches} \]
Now that we have the surface area of the box, we can calculate how much cardboard Cherese will have left over. She purchases 500 square inches of cardboard.
Left over cardboard = Total cardboard purchased - Surface area of the box \[ \text{Left over} = 500 - 446 = 54 \text{ square inches} \]
Thus, the amount of cardboard left over is 54 in.².