The diameter of a copper sphere is 18 , cm. T | vedclass

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(D) The volume of the sphere is given by $V = \frac{4}{3} \pi r^3$,where $r$ is the radius of the sphere.Given diameter $= 18 \, cm$,so radius $r = 9

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$0.6$

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(D) The volume of the sphere is given by $V = \frac{4}{3} \pi r^3$,where $r$ is the radius of the sphere.Given diameter $= 18 \, cm$,so radius $r = 9 \, cm$.Volume $= \frac{4}{3} 	imes \pi 	imes (9)^3 = \frac{4}{3} 	imes \pi 	imes 729 = 972 \pi \, cm^3$.The wire is a cylinder with length $h = 108 \, m = 10800 \, cm$.Let the radius of the wire be $R \, cm$.The volume of the wire is $\pi R^2 h = \pi R^2 	imes 10800$.Since the volume remains constant,$\pi R^2 	imes 10800 = 972 \pi$.$R^2 = \frac{972}{10800} = 0.09$.$R = \sqrt{0.09} = 0.3 \, cm$.The diameter of the wire is $2R = 2 	imes 0.3 = 0.6 \, cm$.

The diameter of a copper sphere is $18 \, cm$. The sphere is melted and drawn into a long wire of uniform circular cross-section. If the length of the wire is $108 \, m$,the diameter of the wire is ....... $cm$.

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