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?(1 point) Responses 406 in.2 406 in. squared 54 in.2 54 in. squared 446 in.2 446 in. squared 426 in.2
The surface area of the box can be calculated by summing the areas of each side. The top and bottom have the dimensions of the length and width (10 x 9 = 90 square inches each), the front and back have the dimensions of the length and height (10 x 7 = 70 square inches each), and the sides have the dimensions of the width and height (9 x 7 = 63 square inches each).
Therefore, the surface area of the box is 2(90) + 2(70) + 2(63) = 180 + 140 + 126 = 446 square inches.
If Cherese purchases 500 square inches of cardboard and the surface area of the box is 446 square inches, she will have 500 - 446 = 54 square inches leftover.
So, the correct response is 54 in.2.