An open-top box has a square base and must contain of volume

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

An open-top box has a square base and must contain

32\text{ cm}^3

of volume. What should be the length of a side of the base, in centimeters, to minimize the amount of material used? (a)

8

(b)

2

(c)

4

(d)

\sqrt[3]{32}