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 1

${\huge {\sf {\bf {\underline {\blue {Answer}}}}}}$

Given :-

• Height of the cone = 1 cm

• Radius of cone = 1 cm

• Radius of hemisphere = 1 cm

To Find :-

• The Volume of solid in terms of ${\sf \pi}$

Solution :-

Calculate Volume of cone

${\boxed {\bf {Volume~ of~ cone = \dfrac {1}{3} \pi {r}^{2} h }}}$

$\rightarrow {\sf {Volume~ of~ cone = \dfrac {1}{3} \times \pi \times {1}^{2} \times 1 }}$

$\rightarrow {\sf {Volume~ of~ cone = \dfrac {1}{3} \pi ~ {cm}^{3} }}$

Calculate Volume of hemisphere

${\boxed {\bf {Volume~ of~ hemisphere = \dfrac {2}{3} \pi {r}^{3}}}}$

$\rightarrow {\sf {Volume~ of~ hemisphere = \dfrac {2}{3} \times \pi \times {1}^{3} }}$

$\rightarrow {\sf {Volume~ of~ hemisphere = \dfrac {2}{3} \pi ~ {cm}^{3} }}$

Total volume of the solid = Volume of cone + Volume of hemisphere

$\rightarrow$ Total volume of the solid = ${\sf \dfrac {1}{3} \pi + \dfrac {2}{3} \pi }$

$\rightarrow$ Total volume of the solid = ${\sf \dfrac {3}{3} \pi }$

$\rightarrow$ Total volume of the solid = ${\sf \dfrac { \cancel {3}}{ \cancel {3}} \pi }$

${\underline {\boxed {\sf {Total~ volume~ of~ the~ solid = \pi ~ {cm}^{3} }} } }$

${\underline {\sf {\purple {Hence,~ the ~ total~ volume~ of~ the~ solid~ is~ \pi ~ {cm}^{3}}}}}$