The radius of a sphere is 6, cm. It is melted | vedclass

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(A) For the given sphere,radius $(r) = 6\, cm$.For the given cylindrical wire,the diameter is $1\, cm$,so the radius $(R) = \frac{1}{2}\, cm$.Let the

Vedclass · Accepted Answer

$11.52$

Vedclass · Answer

(A) For the given sphere,radius $(r) = 6\, cm$.For the given cylindrical wire,the diameter is $1\, cm$,so the radius $(R) = \frac{1}{2}\, cm$.Let the length of the wire be $H\, cm$.Since the volume remains constant when the sphere is melted and recast into a wire:Volume of cylinder = Volume of sphere$\pi R^2 H = \frac{4}{3} \pi r^3$Substituting the values:$R^2 H = \frac{4}{3} r^3$$(\frac{1}{2})^2 	imes H = \frac{4}{3} 	imes (6)^3$$\frac{1}{4} 	imes H = \frac{4}{3} 	imes 216$$\frac{1}{4} 	imes H = 4 	imes 72$$\frac{1}{4} 	imes H = 288$$H = 288 	imes 4 = 1152\, cm$.To convert the length into meters:$H = \frac{1152}{100} = 11.52\, m$.Thus,the length of the wire is $11.52\, m$.

The radius of a sphere is $6\, cm$. It is melted and drawn into a wire of diameter $1\, cm$. Find the length of the wire (in $m$).

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