An wooden toy is made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is $ 10 \mathrm{~cm} $, and its base is of radius $ 3.5 $ $ \mathrm{cm} $, find the volume of wood in the toy. (Use $ \pi=22 / 7 $ )

Given:

A wooden toy is made by scooping out a hemisphere of the same radius from each end of a solid cylinder.

The height of the cylinder is \( 10 \mathrm{~cm} \), and its base is of radius \( 3.5 \) \( \mathrm{cm} \).

To do:

We have to find the volume of wood in the toy.

Solution:

Height of the cylindrical part $h= 10\ cm$

Radius of the base $r = 3.5\ cm$

Therefore,

Volume of the cylindrical part $=\pi r^{2} h$

$=\frac{22}{7}(3.5)^{2} \times 10$

$=\frac{22}{7} \times 12.25 \times 10$

$=385 \mathrm{~cm}^{3}$ Volume of each hemispherical end $=\frac{2}{3} \pi r^{3}$

$=\frac{2}{3} \times \frac{22}{7} \times (\frac{7}{2})^3$

$=\frac{539}{6}$

$=89.83 \mathrm{~cm}^{3}$

The volume of wood in the toy $=$ Volume of the cylindrical part $+2\times$ Volume of each hemispherical end

$=385+2\times 89.83$

$=564.66 \mathrm{~cm}^{3}$

The volume of wood in the toy is $564.66\ cm^3$.

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Updated on: 10-Oct-2022

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