Mathematics

Problem

A beverage company must manufacture open-top cylindrical cups that hold exactly 355 cm

^3

of liquid. For such a cup, the derivative of the total material area with respect to the radius is

S'(r)=4\pi r-\frac{710}{r^{2}}.

Which value of

r

(in cm) will minimize the amount of material used? a)

3.1\text{ cm}

5.6\text{ cm}

3.8\text{ cm}

7.5\text{ cm}