A metallic sphere of radius 6 , cm is melted | vedclass

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Question

(A) The volume of the metallic sphere is given by $V = \frac{4}{3} \pi r^3$,where $r = 6 \, cm$.$V = \frac{4}{3} 	imes \pi 	imes (6)^3 = \frac{4}{3}

Vedclass · Accepted Answer

$11.52$

Vedclass · Answer

(A) The volume of the metallic sphere is given by $V = \frac{4}{3} \pi r^3$,where $r = 6 \, cm$.$V = \frac{4}{3} 	imes \pi 	imes (6)^3 = \frac{4}{3} 	imes \pi 	imes 216 = 288 \pi \, cm^3$.The wire is in the shape of a cylinder with diameter $1 \, cm$,so the radius $R = 0.5 \, cm = \frac{1}{2} \, cm$.Let the length of the wire be $h$. The volume of the wire is $V = \pi R^2 h$.Equating the volumes: $288 \pi = \pi 	imes (\frac{1}{2})^2 	imes h$.$288 = \frac{1}{4} 	imes h$.$h = 288 	imes 4 = 1152 \, cm$.Since $100 \, cm = 1 \, m$,the length in metres is $1152 / 100 = 11.52 \, m$.

$A$ metallic sphere of radius $6 \, cm$ is melted and recast into a wire with diameter $1 \, cm$. Find the length of the wire in metres.

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