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      Question

      A maximum-size sphere is cut from a hemisphere of radius

      r. Find the ratio of the volume of the sphere to the hemisphere. Radius of Hemisphere = 
      A 4:1 Correct Answer Incorrect Answer
      B 3:2 Correct Answer Incorrect Answer
      C 1:4 Correct Answer Incorrect Answer
      D 2:3 Correct Answer Incorrect Answer

      Solution

       Radius of sphere = r/2 Volume of sphere = 4/3 π r³/8 Equate both the volumes: Hemisphere   =    Sphere (2/3) πr³= (4/3) π r³/8 1      = 1/4 =4: 1 The ratio of the volume of the sphere to the hemisphere = 1: 4

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