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in Surface Areas And Volumes by (56.3k points)

The diameter of a metallic sphere is equal to 9 cm. It is melted and drawn into a long wire of diameter 2 mm having uniform cross-section. Find the length of the wire.

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Best answer

Given,

Radius of the sphere = 9/2 cm

So, its volume = 4/3 πr3 = 4/3 π(9/2)3

And, the radius of the wire = 2 mm = 0.2 cm

Let the length of the wire = h cm

So, the volume of wire = πr2h = π(0.2)2h

Then, according to the question we have

Volume of wire = Volume of sphere

π(0.2)2h = 4/3 π(9/2)3

h = 4 x 729/ (3 x 8 x 0.01) = 12150 cm

Therefore, the length of the wire = 12150 cm

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