How many balls of radius 0.5, cm can be produ | vedclass

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(D) The volume of the metallic cylinder is given by $V_{cylinder} = \pi r^2 h = \pi 	imes (4)^2 	imes 3 = 48\pi\, cm^3$.The volume of one spherical

Vedclass · Accepted Answer

$288$

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(D) The volume of the metallic cylinder is given by $V_{cylinder} = \pi r^2 h = \pi 	imes (4)^2 	imes 3 = 48\pi\, cm^3$.The volume of one spherical ball is given by $V_{ball} = \frac{4}{3} \pi r^3 = \frac{4}{3} 	imes \pi 	imes (0.5)^3 = \frac{4}{3} 	imes \pi 	imes 0.125 = \frac{0.5}{3}\pi = \frac{1}{6}\pi\, cm^3$.The number of balls produced is $n = \frac{V_{cylinder}}{V_{ball}} = \frac{48\pi}{\frac{1}{6}\pi} = 48 	imes 6 = 288$.

How many balls of radius $0.5\, cm$ can be produced by melting a metallic cylinder with radius $4\, cm$ and height $3\, cm$?

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