Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.


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Answer:

6 : π

Step by Step Explanation:
  1. Let the radius of the sphere which fits exactly into a cube be r units.
    Then, length of each of edge of the cube = 2r units.
  2. Let V1 and V2 be the volumes of the cube and sphere respectively.

    Then,
    V1 = (2r)3 and V2=  
    4
    3
     πr2
  3. Therefore,  
    V1
    V2
     =  
    (2r)3
     
    4
    3
      πr3
      =  
    8r3
     
    4
    3
      πr3
      =  
    6
    π
     
  4. Thus, V1 : V2= 6 : π

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