A metallic sphere with radius 42, cm is melte | vedclass

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Question

(A) Let the radius of the large metallic sphere be $r = 42\, cm$ and the radius of each small ball be $R\, cm$.The volume of the large sphere is equal

Vedclass · Accepted Answer

$2.1$

Vedclass · Answer

(A) Let the radius of the large metallic sphere be $r = 42\, cm$ and the radius of each small ball be $R\, cm$.The volume of the large sphere is equal to the total volume of the $8000$ small balls.Volume of sphere $= \frac{4}{3} \pi r^3$Volume of $8000$ balls $= 8000 	imes \frac{4}{3} \pi R^3$Equating the volumes: $8000 	imes \frac{4}{3} \pi R^3 = \frac{4}{3} \pi r^3$$8000 R^3 = r^3$$8000 R^3 = (42)^3$$R^3 = \frac{42 	imes 42 	imes 42}{8000}$$R^3 = \left(\frac{42}{20}ight)^3$$R = \frac{42}{20} = 2.1\, cm$Thus,the radius of each small ball is $2.1\, cm$.

$A$ metallic sphere with radius $42\, cm$ is melted to cast $8000$ identical balls. Find the radius of these balls (in $cm$).

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