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The radius of a sphere is 3 cm. It is heated and drawn into a wire of radius 0.1 cm. The length of the wire is ____.

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Detailed Solution

The radius of a sphere is 3 cm. It is heated and drawn into a wire of radius 0.1 cm. The length of the wire is 3600 cm.
Given, the radius of a sphere is 3 cm. It is heated and drawn into a wire of radius 0.1 cm.
When we cast a solid to another their volumes are equal.
So, the volume of the sphere = volume of the wire (cylinder).

\frac{4}{3} π r^{3} = π R^{2} H

\frac{4}{3} π {(3)}^{3} = π {(0.1)}^{2} H

H = \frac{36}{0.01} = 3600 cm

So, the length of the wire is 3600 cm.
Hence, the correct answer is 3600 cm.

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