An open-top box with a square base is to be constructed from 200 square inches of…

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

Problem

An open-top box with a square base is to be constructed from 200 square inches of cardboard. If the base has side length

s

inches, which value of

s

maximizes the volume of the box? (a)

\sqrt{\dfrac{100}{3}}

(b)

\sqrt{\dfrac{200}{3}}

(c)

5\sqrt{2}

(d)

\sqrt{\dfrac{50}{3}}