Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make.
A)x = 46 inches, y = 46 inches, z = 46 inches
B)x = 32 inches, y = 32 inches, z = 32 inches
C)x = 41 inches, y = 41 inches, z = 41 inches
D)x = 45 inches, y = 45 inches, z = 45 inches
E)x = 34 inches, y = 34 inches, z = 34 inches

Question

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make. ​
A)x = 46 inches, y = 46 inches, z = 46 inches
B)x = 32 inches, y = 32 inches, z = 32 inches
C)x = 41 inches, y = 41 inches, z = 41 inches
D)x = 45 inches, y = 45 inches, z = 45 inches
E)x = 34 inches, y = 34 inches, z = 34 inches

Quizplus · Accepted Answer

The box that requires the least amount of material for a given volume is a cube. The volume of a cube is given by V = s^3, where s is the side length. Solving 32,768 = s^3 gives s = 32, so the dimensions are 32 inches by 32 inches by 32 inches.

Find the Values for Each of the Dimensions of a Closed-Top