Question

A steel drum in the shape of a right circular cylinder is required to have a volume of 100 cubic feet. express the amount of material required to make the drum as a function of the radius r of the cylinder. also how much material is required if the drum is of radius 3 feet?

Answer 1

V = pi r^2 h
h = V/pi*r^2 = 100/(pi*r^2)
A = 2pi*rh + 2pir^2
A = 2*pi*r*100/(pi*r^2) + 2pi*r^2
= 200/r + 2pi*r^2

A(3) = 200/3 + 2pi*9 = 123.2 ft^2