Campbell’s Soup Company requires that is its tomato soup containers have a capacity of 64 in^3 , have the shape of a circular cylinder, and be made of aluminum. Determine the radius and height of the container that requires the least amount of metal.

Answer 1

v = πr^2h = 64, so h = 64/(πr^2)
a = 2πr^2 + 2πrh
= 2πr^2 + 128/r

da/dr = 4πr - 128/r^2
= (4πr^3-128)/r^2

Now set da/dr=0 to find minimum area.