Question
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1 \ cm$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.
✓
Answer
For Hemisphere,
Radius$(r) = 1 \ cm$
$\therefore $ Volume $= \frac { 2 } { 3 } \pi r ^ { 3 }$
$= \frac { 2 } { 3 } \pi ( 1 ) ^ { 3 }$
$= \frac { 2 } { 3 } \pi \mathrm { cm } ^ { 3 }$
For cone,
Radius of the base$(r) = 1 \ cm$
Height $(h) = 1 \ cm$
$\therefore $ Volume$= \frac { 1 } { 3 } \pi r ^ { 2 } h$
$= \frac { 1 } { 3 } \pi ( 1 ) ^ { 2 } ( 1 ) = \frac { 1 } { 3 } \pi \operatorname { cm } ^ { 3 }$
Therefore, volume of the solid
=volume of the hemisphere + volume of cone
$= \frac { 2 } { 3 } \pi + \frac { 1 } { 3 } \pi = \pi \mathrm { cm } ^ { 3 }$
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