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 54 in.2 54 in. squared 406 in.2 406 in. squared 446 in.2 446 in. squared 426 in.2
To find the surface area of the box, we need to calculate the surface area of each side and then add them all up.
- The front and back sides of the box have dimensions of 10 inches by 7 inches, so their combined surface area is 2 * (10 * 7) = 140 square inches.
- The top and bottom sides of the box have dimensions of 9 inches by 7 inches, so their combined surface area is 2 * (9 * 7) = 126 square inches.
- The left and right sides of the box have dimensions of 9 inches by 10 inches, so their combined surface area is 2 * (9 * 10) = 180 square inches.
Adding all these up, we get a total surface area of 140 + 126 + 180 = 446 square inches.
Since Cherese purchased 500 square inches of cardboard, subtracting the surface area of the box from the total cardboard she purchased gives us 500 - 446 = 54 square inches remaining.
Therefore, Cherese will have 54 square inches of cardboard left over.