# Thread: Sphere inscribed in cone problem

1. ## 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

2. Hi,

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

Which one do you mean (see attached image)?

3. 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:

4. 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.

5. 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?

6. 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.

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# ratio of sphere inisde cone

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