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?