Cherese 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
To find the amount of cardboard that Cherese needs to build the box, we need to find the surface area of the box. This can be found by adding up the areas of all six sides:
Surface area = 2(10 x 9) + 2(10 x 7) + 2(9 x 7)
Surface area = 180 + 140 + 126
Surface area = 446 square inches
So, Cherese needs 446 square inches of cardboard to build the box. If she purchases 500 square inches of cardboard, she will have 500 - 446 = 54 square inches of cardboard left over.
To find out how much cardboard will be left over, we need to calculate the total surface area of the box and subtract it from the total area of the purchased cardboard.
The surface area of the box is the sum of the areas of all its sides. We have the length (L), width (W), and height (H) of the box. So, we can calculate:
Surface area of the box = 2(LW) + 2(LH) + 2(WH)
Given:
Length (L) = 10 inches
Width (W) = 9 inches
Height (H) = 7 inches
Surface area of the box = 2(10 * 9) + 2(10 * 7) + 2(9 * 7)
= 2(90) + 2(70) + 2(63)
= 180 + 140 + 126
= 446 square inches
Now, we subtract the surface area of the box from the total purchased cardboard area to find how much will be left over:
Leftover cardboard = Total purchased cardboard - Surface area of the box
Leftover cardboard = 500 square inches - 446 square inches
Leftover cardboard = 54 square inches
Therefore, Cherese will have 54 square inches of cardboard leftover.