Question

A company needs to make a cylindrical can that can hold precisely 2.1 liters of liquid. If the entire can is to be made out of the same material, find the dimensions of the can that will minimize the cost. Round your answer to the nearest four decimal places.

Answer 1

area = A = 2 pi r h + 2 pi r^2

2.1 liters = .0021 m^3

.0021 = pi r^2 h
so
h = .0021/(pi r^2)

so
A = 2 pi r (.0021)/(pi r^2) + 2 pi r^2
or
A = .0042/r + 2 pi r^2
for min area dA/dr = 0
0 = -.0042/r^2 + 4 pi r

4 pi r^3 = .0042

r = .0694 meters or 6.94 cm
then h = .139 meters or 13.9 cm