A metallic sphere with radius 6 , cm is melte | vedclass

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

Vedclass · Accepted Answer

$18$

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(D) The volume of the metallic sphere is given by the formula $V = \frac{4}{3} \pi r^3$,where $r = 6 \, cm$.$V = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) = 288 \pi \, cm^3$.The wire is in the shape of a cylinder with radius $R = 0.4 \, cm$ and length $h$. The volume of the wire is $V = \pi R^2 h$.Since the volume remains constant during the process of melting and recasting,we have:$288 \pi = \pi (0.4)^2 h$$288 = 0.16 	imes h$$h = \frac{288}{0.16} = \frac{28800}{16} = 1800 \, cm$.To convert the length into metres,we divide by $100$:$h = \frac{1800}{100} = 18 \, m$.

$A$ metallic sphere with radius $6 \, cm$ is melted and recast into a wire of radius $0.4 \, cm$. Find the length of the wire in metres.

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