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Question

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is:

A
12 m
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B
18 m
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C
36 m
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D
66 m
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Solution

The correct option is C 36 m
Diameter of metallic sphere=6 cm
Radius of metallic sphere=3 cm
Also, we have diameter of cross-section of cylindrical wire=0.2 cm
Radius of cross-section of cylinrical wire=0.1 cm
Let the length of the wire be h cm
Since metallic sphere is converted into a cylinder shaped wire of length h cm
Volume of the metal used in wire = Volume of the sphere

π×r2s×h=43×π×r3c

π×(110)2×h=43×π×27

π×1100×h=36π

h=36π×100πcm=3600 cm=36 metres

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