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(B) The volume of the cylinder is given by $V_{cylinder} = \pi r^2 h$. Given diameter $= 1 \, cm$,so radius $r = 0.5 \, cm = \frac{1}{2} \, cm$ and he

Vedclass · Accepted Answer

$384$

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(B) The volume of the cylinder is given by $V_{cylinder} = \pi r^2 h$. Given diameter $= 1 \, cm$,so radius $r = 0.5 \, cm = \frac{1}{2} \, cm$ and height $h = 4 \, cm$. $V_{cylinder} = \pi 	imes (\frac{1}{2})^2 	imes 4 = \pi 	imes \frac{1}{4} 	imes 4 = \pi \, cm^3$. The volume of one spherical ball is $V_{sphere} = \frac{4}{3} \pi r^3$. Given radius $r = \frac{1}{8} \, cm$. $V_{sphere} = \frac{4}{3} 	imes \pi 	imes (\frac{1}{8})^3 = \frac{4}{3} 	imes \pi 	imes \frac{1}{512} = \frac{\pi}{3 	imes 128} = \frac{\pi}{384} \, cm^3$. The number of balls produced is $n = \frac{V_{cylinder}}{V_{sphere}} = \frac{\pi}{\frac{\pi}{384}} = 384$.

$A$ metallic cylinder with diameter $1 \, cm$ and height $4 \, cm$ is melted and recast to produce balls of radius $\frac{1}{8} \, cm$. Find the number of balls produced.

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