Minimizing surface area for a closed cylindrical can (using variables)

Question

I am not sure how to approach this problem...

"Find the dimensions of the closed cylindrical can that will have a capacity of k units of volume and will use the minimum amount of material. Find the ratio of the height h to the radius r of the top and bottom.

Any help would be appreciated.

Answer 1

HINT

We have

• volume $V=\pi R^2H=k$ as constraint

• surface $S=2\pi R^2+2\pi RH$ to minimize