How many balls of radius 1.4 , cm can be prod | vedclass

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(C) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Let $R$ be the radius of the large metallic sphere $(R = 42 \, cm)$ and $

Vedclass · Accepted Answer

$27000$

Vedclass · Answer

(C) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Let $R$ be the radius of the large metallic sphere $(R = 42 \, cm)$ and $r$ be the radius of the small ball $(r = 1.4 \, cm)$.The number of balls $n$ that can be produced is given by the ratio of the volume of the large sphere to the volume of one small ball:$n = \frac{\frac{4}{3} \pi R^3}{\frac{4}{3} \pi r^3} = \left( \frac{R}{r} \right)^3$.Substituting the values:$n = \left( \frac{42}{1.4} \right)^3 = (30)^3$.$n = 27,000$.Therefore,$27,000$ balls can be produced.

How many balls of radius $1.4 \, cm$ can be produced by melting a metallic sphere of radius $42 \, cm$?

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