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 $\pi$.

Given:

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.

To do:

We have to the volume of the solid in terms of $\pi$.

Solution:

Radius of the hemisphere $=1 \mathrm{~cm}$

Height of the conical part

$=1 \mathrm{~cm}$

This implies,

Total height of the solid $=1+1=2 \mathrm{~cm}$

Therefore,

Volume of the solid $=$ Volume of the conical part $+$ Volume of the hemispherical part

$=\frac{1}{3} \pi r^{2} h+\frac{2}{3} \pi r^{3}$

$=\frac{1}{3} \pi r^{2}(h+2 r)$

$=\frac{1}{3} \pi \times(1)^{2}[1+2 \times1]$

$=\frac{\pi}{3} \times 1 \times 3$

$=\pi \mathrm{~cm}^{3}$

The volume of the solid is $\pi\ cm^3$.

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Updated on: 10-Oct-2022

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