A sphere and a right circular cylinder have the same radius. If the volume of the sphere is double of the volume of the cylinder, what is the ratio of the height of the cylinder to its radius?


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Answer:

2:3

Step by Step Explanation:
  1. The volume of a sphere of radius 'r' =  
    4
    3
     πr3
  2. The volume of a cylinder of radius 'r' and height 'h' = πr2h
  3. Here, we are told the the volume of the sphere is double of the volume of the cylinder.
    So,  
    4
    3
     πr3 = 2 × (πr2h)
  4. Solving the above equation, we get 3h = 2r.
  5. Therefore, the ratio of the height of the cylinder to its radius is 2:3.

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