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Question

If a sphere is inscribed in a cube, find the ratio of the volume of the cube to the volume of the sphere.
 


Solution

 Let edge of a cube = a 

then its volume =a3

  A sphere is inscribed in the cube 

Diameter of sphere =a

 and radius =(a2)

 Volume of sphere=43πr3

=43π(a2)2

=43π×a38

=πa36

 Now ratio between their volumes  

=a3:πa36

=6a3:πa3

=6:π
 

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