Hello, philipsach1!

Did you make a sketch?

[I] Determine the dimensions of the cone of maximum volume

that can be inscribed in a sphere with radius 3? Code:

A
* * *
* /:\ *
* / : \ *
* / : \ *
/ :3 \
* / : \ *
* / O* \ *
* / 3* : *3 \ *
/ * y: * \
B *- - - - + - - - -* C
* : x *
* : *
* * *

The center of the sphere is

is the side view of the cone.

Note that:

The volume of a cone is: . **[1]**

In the diagram, we see that:

So we have: . **[2]**

The diagram also tells us that: .

Substitute into **[2]**: .

Can you finish up?