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Math Help - Sphere inscribed in cone problem

  1. #1
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    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
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  2. #2
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    Hi,

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

    Which one do you mean (see attached image)?
    Attached Thumbnails Attached Thumbnails Sphere inscribed in cone problem-sphereincone.gif  
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  3. #3
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    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:
    Attached Thumbnails Attached Thumbnails Sphere inscribed in cone problem-sphere-cone.jpg  
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  4. #4
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    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.
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  5. #5
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    Quote Originally Posted by Andreas Goebel View Post
    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?
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  6. #6
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    Quote Originally Posted by galactus View Post
    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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