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InterviewSolution
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What will be the ratio of the volumes of a solid cone , a solid hemisphere and a solid cylinder when their radii of bases and heights are equal ? |
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Answer» Let radius of the cone , hemisphere and cylinder be r unit and their equal heights be h unit . Since the heights of the three objects are equal , ` :. ` height of the cone = height of the cylinder = height of the hemisphere = radius of the hemisphere : volume of the cylinder ` = 1/3 pir^(2) h : 2/3 pir^(3) : pir^(2) h ` ` = 1/3 pi r^(2) . r , 2/3 pir^(3) : pir^(2) r ` ` = 1/3 pi r^(3) : 2/3 pir^(3) : pir^(3) ` ` = 1/3 : 2/3 : 1 ` = 1: 2 : 3 Hence the required ratio is 1 : 2 : 3 |
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