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Thread: Finding radius of a sphere inside a cone

  1. #1
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    Finding radius of a sphere inside a cone

    I am trying to solve a problem that I just can't figure out. Here it is: A cone is filled with water. 2 spheres are firmly submerged into the cone. The larger sphere's radius is twice that of the smaller sphere. The volume of water that still remains after the spheres are submerged is 2016pi. What is the radius of the smaller sphere?
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  2. #2
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    Re: Finding radius of a sphere inside a cone

    Hey mrscann.

    Can you show us what you have tried?

    You might also want to draw a picture if it's too confusing.
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  3. #3
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    Re: Finding radius of a sphere inside a cone

    Quote Originally Posted by mrscann View Post
    A cone is filled with water. 2 spheres are firmly submerged into the cone. The larger sphere's radius is twice that of the smaller sphere. The volume of water that still remains after the spheres are submerged is 2016pi. What is the radius of the smaller sphere?
    Using similar triangles and Pythagoras, I get a nice value for r

    R = cone base radius

    r = small sphere radius

    S = cone slant height

    y = distance from bottom of the small sphere to the cone's vertex
    Attached Thumbnails Attached Thumbnails Finding radius of a sphere inside a cone-spheres_in_cone.jpg  
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