Question

A company plans to manufacture a container having the shape of a right circular cylinder, open at the top, and having a capacity of 24pi cubic inches. If the cost of the material for the bottom is $.30 per square inch and that for the curved sides is $.10 per square inch, express the total cost C of the material as a function of the radius r of the base of the container.

Answer 1

C = .30*pi r^2 + .1* 2 pi r h

pi r^2 h = 24 pi
r^2 h = 24
h = 24/r^2

C = .30 pi r^2 + .2 pi r (24)/r^2
C = pi (.3 r^2 + 4.8/r)

Answer 2

Did they not ask for r and h for minimum cost?

Answer 3

No. This is exactly how the question was presented.

Answer 4

OK, wait til next year :)