If a hemisphere and a cylinder stand on equal base and have the same height, find the ratio of their volumes.


Answer:

^@2:3^@

Step by Step Explanation:
  1. The volume of a cylinder of radius ^@r^@ and height ^@h^@ is ^@ \pi r^2h.^@
  2. The volume of a hemisphere of radius ^@r^@ is ^@\dfrac {2} {3} \pi r^3^@.
  3. ^@\begin{align} \dfrac { \text { Volume of hemisphere } } { \text { Volume of cylinder } } & = \dfrac { \dfrac {2} {3} \pi r^3 }{ \pi r^2h } \space [\because r = h] \\ & = \dfrac { 2 } { 3 } \end{align}^@
    So, the ratio of their volumes will be . Cancelling out the equal terms we find the ratio as ^@2:3^@.

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