How many balls with diameter 1 , cm can be pr | vedclass

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(B) The volume of the metallic cylinder is given by $V_{cylinder} = \pi r^2 h = \pi 	imes (6)^2 	imes 4 = 144\pi \, cm^3$.The diameter of each ball

Vedclass · Accepted Answer

$864$

Vedclass · Answer

(B) The volume of the metallic cylinder is given by $V_{cylinder} = \pi r^2 h = \pi 	imes (6)^2 	imes 4 = 144\pi \, cm^3$.The diameter of each ball is $1 \, cm$,so the radius $r_{ball} = 0.5 \, cm$.The volume of one spherical ball is $V_{ball} = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (0.5)^3 = \frac{4}{3} \pi (0.125) = \frac{0.5}{3} \pi = \frac{1}{6} \pi \, cm^3$.The number of balls produced is $n = \frac{V_{cylinder}}{V_{ball}} = \frac{144\pi}{\frac{1}{6}\pi} = 144 	imes 6 = 864$.

How many balls with diameter $1 \, cm$ can be produced by melting a metallic cylinder with radius $6 \, cm$ and height $4 \, cm$?

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