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A hemispherical bowl of internal diameter $36\ cm$ contains liquid. This liquid is filled into $72$ cylindrical bottles of diameter $6\ cm$. Find the height of each bottle, if $10\%$ liquid is wasted in this transfer.
Given: A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. 10% liquid is wasted in this transfer.
To do: To Find the height of each bottle
Solution:
Internal diameter of the bowl $= 36\ cm$
Internal radius of the bowl, $r = \frac{36}{2}=18\ cm$
Volume of the liquid, $V=\frac{2}{3} \pi r^{3} =\frac{2}{3} \times \pi \times 18^{3} =3888\pi \ cm^{3}$
10% of the liquid wasted$=\frac{10}{100} \times 3888\pi \ cm^{3} =388.8\pi cm^{3}$
Liquid transferred in the cylindrical bottles$=$Total volume of the liquid-wasted liquid
$=3888\pi -388.8\pi =3499.2\pi \ cm^{3}$
Let the height of the small bottle be $‘h’$.
Diameter of a small cylindrical bottle = 6 cm
Radius of a small bottle, $R = 3\ cm$.
Volume of a single bottle$=\pi R^{2} h=\pi \times 3^{2} \times h=9\pi h\ cm^{3}$
No. of small bottles, $n = 72$
$\therefore \ n\times 9\pi h=3499.2\pi$
$\Rightarrow h=\frac{3499.2\pi }{9\pi \times 72}$
$\Rightarrow h=5.4\ cm$
Therefore, Height of the small cylindrical bottle $=5.4\ cm$
Updated on: 10-Oct-2022
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