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A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find in terms of π, the volume of the solid.
A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find in terms of π, the volume of the solid.
Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20G | ICSE | Selina
A solid is in the form of a cone standing on a hemisphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find in terms of π, the volume of the solid.

Radius of both cone and hemisphere = 8 cm

And, height = 8 cm

\[\begin{array}{*{35}{l}}

Volume\text{ }of\text{ }the\text{ }solid\text{ }=\text{ }Volume\text{ }of\text{ }cone\text{ }+\text{ }volume\text{ }of\text{ }hemisphere  \\

=\text{ }1/3\text{ }\pi {{r}^{2}}h\text{ }+\text{ }2/3\text{ }\pi {{r}^{3}}  \\

=\text{ }1/3\text{ }\pi {{\left( 8 \right)}^{2}}\left( 8 \right)\text{ }+\text{ }2/3\text{ }\pi {{\left( 8 \right)}^{3}}  \\

=\text{ }\pi {{\left( 8 \right)}^{3}}  \\

=\text{ }512\text{ }\pi \text{ }c{{m}^{3}}  \\

\end{array}\]

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