The Diameter Of A Metallic Sphere Is 6 Cm. The Sphere Is Melted And Drawn Into A Wire Of Uniform Circular Cross-section. If The Length Of The Wire Is 36 M, Find The Radius Of Its Cross-section.

Given:

The diameter of a metallic sphere = 6 cm.

The length of the cylindrically shaped wire is 36m

The radius of the sphere =[latex] \frac{6}{2} = 3cm [/latex]

The volume of the sphere = [latex] \frac{4}{3} * \pi * 3^{3}cm^{3} [/latex] [latex] \Rightarrow 36\pi cm^{3} [V = \frac{4}{3}\pi 3^{3}] [/latex]

Let the radius of the cross-section of wire be rcm

The length of the cylindrically shaped wire is 36m

Therefore, the volume of the wire =

[latex] (\pi r^{2} * 3600) cm^{3} [V = \pi r^{2}h] [/latex]

As given in the question, the metallic sphere is converted into cylindrically shaped wire.

Therefore, the Volume of the wire = Volume of the sphere.

[latex] \Rightarrow r^{2} = \frac{36\pi}{3600\pi} = \frac{1}{100} [/latex] [latex] \Rightarrow r = \frac{1}{10}cm = 1mm [/latex]

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