A closed cylindrical can must hold exactly of liquid

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A closed cylindrical can must hold exactly

500\text{ cm}^3

of liquid. The material for the top and bottom costs twice as much per square centimeter as the material for the side. Determine the radius

r

(in centimeters) that minimizes the total material cost.