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(A) Given: Diameter of the metallic sphere $D = 12 \, cm$,so radius $R = 6 \, cm$.Radius of the smaller ball $r = 0.3 \, cm$.Let the number of balls p

Vedclass · Accepted Answer

$8000$

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(A) Given: Diameter of the metallic sphere $D = 12 \, cm$,so radius $R = 6 \, cm$.Radius of the smaller ball $r = 0.3 \, cm$.Let the number of balls produced be $n$.Since the volume remains constant during melting and recasting,the volume of the large sphere equals the sum of the volumes of $n$ small balls.$V_{	ext{large}} = n 	imes V_{	ext{small}}$$\frac{4}{3} \pi R^3 = n 	imes \frac{4}{3} \pi r^3$$R^3 = n 	imes r^3$$n = \frac{R^3}{r^3} = \left( \frac{R}{r} ight)^3$$n = \left( \frac{6}{0.3} ight)^3 = (20)^3$$n = 8000$.Thus,the number of balls produced is $8000$.

$A$ metallic sphere with diameter $12 \, cm$ is melted and identical balls with radius $0.3 \, cm$ are produced. Find the number of balls produced.

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