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whats the problem? we dont all see what you see :)

whose radius? cyl or sphere?

sphere

we can take the cross section and just figure out the rectangle in a circle... right?

do we want to maximize the area of the cyl? or just the height?

Like this: sorry for the cheesy sketch =P

area...volume; same diff :)

So it IS volume we want to maximize....right?

which of these is the radius of the sphere?
\[\sqrt[4]{3} \leftarrow \rightarrow 4\sqrt{3}\]

second one

good :) then we can work this easier :)

the end reply for h=4 cm, since h was divided into two, the height would be 2h, therefore 8 cm =)

4sqrt(3)
------- = 2 sqrt(6); the height for max volume should be 4 sqrt(6)
sqrt(2)

is that the right answer? :)

h=4 cm, height=2h, therefore, maximum height=8 cm

thank you! :)

if I was helpful; youre welcome :)