A hemispherical bowl of internal diameter 54 | vedclass

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Question

(D) The internal radius of the hemispherical bowl is $R = \frac{54}{2} = 27 \ cm$.The volume of the hemispherical bowl is $V_{bowl} = \frac{2}{3} \pi

Vedclass · Accepted Answer

$162$

Vedclass · Answer

(D) The internal radius of the hemispherical bowl is $R = \frac{54}{2} = 27 \ cm$.The volume of the hemispherical bowl is $V_{bowl} = \frac{2}{3} \pi R^3 = \frac{2}{3} \pi (27)^3 \ cm^3$.The volume of one cylindrical bottle is $V_{bottle} = \pi r^2 h = \pi (3)^2 (9) = 81 \pi \ cm^3$.The number of bottles required is given by the ratio of the total volume of the liquid to the volume of one bottle:$	ext{Number of bottles} = \frac{V_{bowl}}{V_{bottle}} = \frac{\frac{2}{3} \pi (27)^3}{\pi (3)^2 (9)} = \frac{2}{3} 	imes \frac{27 	imes 27 	imes 27}{9 	imes 9} = \frac{2}{3} 	imes \frac{19683}{81} = \frac{2}{3} 	imes 243 = 2 	imes 81 = 162$.Therefore,$162$ bottles are required to empty the bowl.

$A$ hemispherical bowl of internal diameter $54 \ cm$ contains a liquid. The liquid is to be filled in cylindrical bottles of radius $3 \ cm$ and height $9 \ cm$. How many bottles are required to empty the bowl?

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