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Probability

Question

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A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.

Solution

V₁ = Volume of the cone

equals space space 1 third πr squared straight h equals space space 1 third πr squared equals space space 1 third πr cubed

V₂ = Volume of the hemisphere

equals 2 over 3 πr cubed

V₃ = Volume of the cylinder = πr²h = πr²r = πr³r

therefore space space space straight V subscript 1 space colon space straight V subscript 2 space colon space straight V subscript 3 space equals 1 third πr cubed space colon 2 over 3 πr cubed colon πr cubed

= 1 : 2 :3

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