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प्रश्न
A hemispherical bowl of internal radius 9 cm is full of liquid . The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm . How many bottles are needed to empty the bowl ?
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उत्तर
The radius of the hemispherical bowl, R = 9 cm
Radius of the cylinderical bottles, r = 1.5 cm
Height of the bottles, h = 4 cm
Let the number of bottles required be n.
Volume of the hemispherical bowl = n × Volume of the cylinderical bottles
\[\frac{\text { Volume of the hemispherical Bowl}}{\text { Volume of the cylinderical bottles}} = n\]
\[ \Rightarrow \frac{\frac{2}{3} \pi R^3}{\pi r^2 h} = n\]
\[ \Rightarrow \frac{\frac{2}{3} \left( 9 \right)^3}{\left( 1 . 5 \right)^2 \left( 4 \right)} = n\]
\[ \Rightarrow 54 = n\]
Hence, the 54 bottles are required.
