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(A) The volume of the material remains constant when a sphere is reshaped into a wire.Radius of the sphere $R = \frac{18}{2} = 9\, cm$.Diameter of the

Vedclass · Accepted Answer

$243$

Vedclass · Answer

(A) The volume of the material remains constant when a sphere is reshaped into a wire.Radius of the sphere $R = \frac{18}{2} = 9\, cm$.Diameter of the wire $= 40\, mm = 4\, cm$,so the radius of the wire $r = \frac{4}{2} = 2\, cm$.Let the length of the wire be $h\, cm$.Volume of the sphere $= \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (9)^3 = \frac{4}{3} \pi (729) = 972\pi\, cm^3$.Volume of the cylindrical wire $= \pi r^2 h = \pi (2)^2 h = 4\pi h\, cm^3$.Equating the volumes: $972\pi = 4\pi h$.$h = \frac{972}{4} = 243\, cm$.Thus,the length of the wire is $243\, cm$.

$A$ copper sphere of diameter $18\, cm$ is drawn into a wire of diameter $40\, mm$. Then,the length of the wire is......$cm$?

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