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A hemispherical bowl of internal radius $ 9 \mathrm{~cm} $ is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius $ 1.5 \mathrm{~cm} $ and height $ 4 \mathrm{~cm} $. How many bottles are needed to empty the bowl?
Given:
A hemispherical bowl of internal radius \( 9 \mathrm{~cm} \) is full of liquid.
The liquid is to be filled into cylindrical shaped bottles each of radius \( 1.5 \mathrm{~cm} \) and height \( 4 \mathrm{~cm} \).
To do:
We have to find the number of bottles needed to empty the bowl.
Solution:
Radius of the hemispherical bowl $r = 9\ cm$
Volume of liquid in the hemispherical bowl $=\frac{2}{3} \pi r^{3}$
$=\frac{2}{3} \pi \times 9^3$
$=486 \pi$
Radius of each cylindrical bottle $R = 1.5\ cm$
Height of each cylindrical bottle $h = 4\ cm$
Volume of each cylindrical bottle $=\pi \mathrm{R}^{2} h$
$=\pi \times (1.5)^2 \times 4$
$=9 \pi$
Number of cylindrical bottles needed to empty the bowl $=\frac{\text { Volume of hemisphere bowl }}{\text { Volume of one cylindrical bottle }}$
$=\frac{486 \pi}{9 \pi}$
$=54$
Hence, 54 bottles are needed to empty the bowl.
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