How many balls with diameter 0.5, cm can be p | vedclass

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(C) The volume of the metallic cylinder is given by $V_{cylinder} = \pi r^2 h$. Substituting $r = 2\, cm$ and $h = 8\, cm$,we get $V_{cylinder} = \pi

Vedclass · Accepted Answer

$1536$

Vedclass · Answer

(C) The volume of the metallic cylinder is given by $V_{cylinder} = \pi r^2 h$. Substituting $r = 2\, cm$ and $h = 8\, cm$,we get $V_{cylinder} = \pi 	imes (2)^2 	imes 8 = 32\pi\, cm^3$.The volume of one spherical ball with diameter $0.5\, cm$ (radius $r_b = 0.25\, cm = 1/4\, cm$) is $V_{ball} = \frac{4}{3} \pi r_b^3 = \frac{4}{3} \pi (1/4)^3 = \frac{4}{3} \pi 	imes \frac{1}{64} = \frac{\pi}{48}\, cm^3$.The number of balls produced is $n = \frac{V_{cylinder}}{V_{ball}} = \frac{32\pi}{\pi/48} = 32 	imes 48 = 1536$.

How many balls with diameter $0.5\, cm$ can be produced by melting a metallic cylinder with radius $2\, cm$ and height $8\, cm$?

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