Hello, galactus!

I *think* I've got a handle on this one . . .

We've all seen the classic 'sphere inside a cone', 'cylinder in a cone',

'cone in a sphere' problems, etc.

Here's one that is a little different if anyone would enjoy tackling it.

Let's orient the ellipsoid 'horizontally' . . . then we have: Code:

- *
: /|\
: / | \
: / | \
: / | \
H / ..*.. \
: /*::::|::::*\
: *-:-:-:+ - a -*
: / *::::b::::* \
- *- - - - * - - - -*
: R :

From similar right triangles, we have: .

The volume of this ellipsoid of revolution is: .

Substitute [1] into [2]: .

Maximize: .

Substitute into [2]: .