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A sphere is inscribed in a cone with height 4 and base radius 3. What is the ratio of the volume of the sphere to the volume of the cone?

Guest Oct 16, 2017
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Here's the cross-section pic  :

 

 

 

 

The radius of the sphere  1.5  units

The volume of the cone is   pi (3)^2 *4 / 3   units^3  =  12pi  units^3

The volume of the sphere is (4/3)pi (1.5)^3  units^3 = 4.5 units^3

 

So   ratio  of the volume of the sphere to the cone is :

 

4.5 pi  / 12 pi  =    4.5 / 12  =      (9/2) / (24/2)  =  9 / 24  =  3 / 8

 

 

cool cool cool

CPhill  Oct 16, 2017

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