Hello,

The volume of a cylindre is calculated by:

You've got the additional condition:

Solve this equation for h:

. Now plug in this term for h into the first equation and expand:

The volume has an extreme value if the first derivative equals zero:

Now solve the equation V'(r) = 0 for r. You'll get r = 0. This kite has the volume zero, which is indeed an extremum. The 2nd value for r is:

The maximal volume is

EB