A metallic sphere of radius 21 ,cm is melted | vedclass

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Question

(D) The volume of the metallic sphere is given by the formula $V = \frac{4}{3} \pi r^3$,where $r = 21 \,cm$.$V = \frac{4}{3} 	imes \pi 	imes (21)^3

Vedclass · Accepted Answer

$493.92$

Vedclass · Answer

(D) The volume of the metallic sphere is given by the formula $V = \frac{4}{3} \pi r^3$,where $r = 21 \,cm$.$V = \frac{4}{3} 	imes \pi 	imes (21)^3 = 4 	imes \pi 	imes 441 	imes 7 = 12348 \pi \,cm^3$.The wire is in the shape of a cylinder with radius $R = 0.5 \,cm$ and length $h$. The volume of the wire is $V = \pi R^2 h$.Equating the volumes: $12348 \pi = \pi 	imes (0.5)^2 	imes h$.$12348 = 0.25 	imes h$.$h = \frac{12348}{0.25} = 12348 	imes 4 = 49392 \,cm$.To convert the length into metres,divide by $100$: $h = \frac{49392}{100} = 493.92 \,m$.

$A$ metallic sphere of radius $21 \,cm$ is melted and recast into a wire with radius $0.5 \,cm$. Find the length of the wire in metres.

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