Suppose Campbell's wants to sell a quantity of soup that has volume 54 cubic inches. It sells its soup in aluminum cans that have the shape of a...

Suppose Campbell's wants to sell a quantity of soup that has volume 54 cubic inches. It sells its soup in aluminum cans that have the shape of a right circular cylinders. Find the radius and the height of the container that would minimalize the materials needed to make the can. Be sure to check that you have minimized the surface area by using the second derivative test. Use hints and show all work.

Hints:

1. Draw a picture and use r for the radius and h for the height. This will match with any formulas you look up.
2. The constraint equation will come from the volume. Need the formula of right cylinder.
3. Then find an equation that represents the surface area of the cylinder and then minimize it.
4. When you find r, round to the nearest whole number.