Solution 1: Let . Then . Taking derivative with respect to r,
. This equals zero when , or when . ∎
Solution 2: Using the method of Lagrange multipliers, there exists a constant with A(r,h) and V(r,h) such that
, therefore
Equating these two,
, finding the actual dimensions follows. ∎
There are probably other solutions involving AM-GM inequality or other techniques. The preferred solution to use is probably dependent on the course you are taking.
