An open topped box with a square base will have volume of 9464 cubic inches and uses 2132 square inches of material. What are the dimensions of the box?
A) 26 in. by 26 in. by 14 in.
B) 52 in. by 52 in. by 3.5 in.
C) 31 in. by 31 in. by 9 in.
D) 13 in. by 13 in. by 56 in.

Question

Quizplus · Accepted Answer

The volume of the box is given by the formula V = lwh, where l = w for a square base, so V = l^2h. Given V = 9464 cubic inches, we can set up the equation l^2h = 9464. The surface area of an open-topped box is given by S = l^2 + 4lh, where S = 2132 square inches. Substituting the values from the volume equation into the surface area equation allows us to solve for l and h. Only option A, with dimensions 26 in. by 26 in. by 14 in., satisfies both the volume and surface area requirements when checked.

An Open Topped Box with a Square Base Will Have