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Q.

A copper sphere of radius 3 cm is melted and drawn into a 72 cm long wire of uniform circular cross-section. Then, its radius is ____.

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Detailed Solution

A copper sphere of radius 3 cm is melted and drawn into a 72 cm long wire of uniform circular cross-section. Then, its radius is 0.707 cm.
Given, radius of the sphere is 3 cm.
We know that the volume of the sphere is

\frac{4}{3} π r^{3}

= \frac{4}{3} π {(3}^{3})

= 113.1 c m^{3}

Wire is in the form of a cylinder.
If the sphere is casted to a cylinder then the volumes are unchanged.
Hence, the volume of cylinder = volume of sphere =

113.1 c m^{3}

.

π r^{2} h = 113.1

π r^{2} (72) = 113.1

r^{2} = 0.5

r = 0.707 cm
So, the radius is 0.707 cm.
Hence, the correct answer is 0.707 cm.

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