A manufacturer wants to design a cylindrical can that holds of liquid

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

Problem

A manufacturer wants to design a cylindrical can that holds

500\,\text{cm}^3

of liquid. The cost of the metal for the side is half the cost per square centimeter of the metal for the top and bottom. Which radius

r

(to the nearest tenth of a centimeter) minimizes the total material cost? (a)

4.3\,\text{cm}

(b)

5.4\,\text{cm}

(c)

3.4\,\text{cm}

(d)

2.7\,\text{cm}