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Question
A sphere and a cone have the same radii. If their volumes are also equal, prove that the height of the cone is twice its radius.
Solution
Let r be the radii of sphere and cone.
Volume of sphere = `4/3pir^3 = 1/3pir^2h` (h = 2r for sphere)
Volume of cone = `1/3pir^2h`
But h = 2r for sphere
Therefore , h = 2r for cone also.
Hence , proved
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