# Sphere inscribed in cone problem

• Dec 3rd 2008, 05:11 PM
KalebKAS
Sphere inscribed in cone problem
This is a sphere inscribed in a cone problem. Given a right circular cone of a given size and shape, what is the radius of a sphere inscribed in the cone? Also, how does the ratio of the sphere's volume vary with the shape of the cone? Any suggestions? Thanks
• Dec 4th 2008, 02:46 AM
Andreas Goebel
Hi,

as far as I understand you there are several solutions to that.

Which one do you mean (see attached image)?
• Dec 4th 2008, 03:50 AM
galactus
I assume you mean the sphere of maximum volume that can be inscribed inside a cone of given radius and what not.

Here is a nice diagram to illustrate:
• Dec 4th 2008, 06:03 AM
KalebKAS
To galactus:

This does make sense... Do you think it relates to 3-D all the same, for the sphere and cone though?? I mean in this case a radius will still be a radius? I just have trouble finding the contruent triangles in the sphere and cone idea because then the congruuent triangles would slices of the cone?? Maybe I'm not seeing it correctly. Thanks.
• Dec 4th 2008, 06:05 AM
KalebKAS
Quote:

Originally Posted by Andreas Goebel
Hi,

as far as I understand you there are several solutions to that.

Which one do you mean (see attached image)?

As far as I understand, the cone can change too so thats why i'm wondering which one to take constant so that I when the cone has certain dimensions, say, except the height h continues to increase/decrease, how does that effect the size of the sphere?
• Dec 4th 2008, 06:10 AM
KalebKAS
Quote:

Originally Posted by galactus
I assume you mean the sphere of maximum volume that can be inscribed inside a cone of given radius and what not.

Here is a nice diagram to illustrate:

Also, this might be a stupid question, but how are the two triangles similar? I know they share an angle, but past that I am not seeing it... Thanks.