A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them is being $ 3.5 \mathrm{~cm} $ and the total height of solid is $ 9.5 \mathrm{~cm} $. Find the volume of the solid. (Use $ \pi=22 / 7) $

Given:

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them is being \( 3.5 \mathrm{~cm} \) and the total height of solid is \( 9.5 \mathrm{~cm} \).

To do:

We have to find the volume of the solid.

Solution:

Radius of the base of the cone $=3.5 \mathrm{~cm}$

Total height of the solid $=9.5 \mathrm{~cm}$

This implies,

Height of the conical part $=9.5-3.5$

$=6 \mathrm{~cm}$

Therefore,

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

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

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

$=\frac{1}{3} \times \frac{22}{7} \times(3.5)^{2}[6+2 \times 3.5]$

$=\frac{22}{21} \times (3.5)^2 \times 13$

$=166.83 \mathrm{~cm}^{3}$

The volume of the solid is $166.83\ cm^3$.

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Updated on: 10-Oct-2022

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