Question

An oil can is to be made in the form of a right circular cylinder to have a volume of 16 pie inches cubed. Find the dimensions of the can that requires the least amount of material

Answer 1

v = pi r^2 h
a = 2 pi r^2 + 2 pi r h

h = 16pi/pi r^2 = 16/r^2

a = 2 pi r^2 + 2 pi r 16/r^2
= 2pi (r^2 + 16/r)

min area when 2r - 16/r^2 = 0

2r^3 - 16 = 0
r = 2

So, the can has a radius of 2 and a height of 4