Question

The marketing manager of a soda drink company wants to design a can woth a height that is four times the radius of the can.

A. Express the volume of tge can as a function of the radius r, f(r)
B. Express the volume of the can as a function of the heighy h, f(h)

Answer 1

Volume of a cylinder:

V = area of the base * height

Area of the base = π(r^2)

A) h = 4r

f(r) = V(r) = [π(r^2) ] h = π(r^2)(4r) = 4π(r^3)

B) h = 4r => r = h/4

f(h) = V(h) = [π(r^2) ] h = [ π(h/4)^2 ]h = [π(h^2)/(16) ]h = π(h^3) / 16