A closed right circular cylinder must contain of liquid

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

Problem

A closed right circular cylinder must contain

1000\,\text{cm}^3

of liquid. The material for the lateral surface costs

0.05

per square centimetre, and the material for the top and bottom costs

0.08

per square centimetre. Let

r

be the radius, in centimetres, of the cylinder. Which of the following is closest to the value of

r

that minimizes the total material cost? (a)

3.7

(b)

4.6

(c)

5.5

(d)

6.3