A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the dimensions of the can that will minimize the amount of material used in its construction.

Answer 1

πr^2 h = 1500 cm^3
h = 1500/(πr^2)
The material used has area
A = 2πr^2 + 2πrh = 2πr^2 + 2πr*1500/(πr^2) = 2πr^2 + 3000/r
dA/dr = 4πr - 3000/r^2
so now just find where dA/dr = 0