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The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. The length of the wire is

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14400 cm

36000 cm

24000 cm

12000 cm

answer is A.

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Detailed Solution

Given, diameter of a sphere is 6 cm and it is melted and drawn into a wire of diameter 0.2 cm.
The volume of material in wire = Volume of the sphere of radius.
Let length of wire be “h”.
We know that the volume of a cylinder

= π × r 2 × h

.
The volume of a sphere is

= 43 × π × r 3

.
Then length of the wire is,

π × (0.1) 2 × h = 4 (43 × π × 33) π h × (0.1) 2 = 4 × 43 × π × 3 × 3 × 3 h = 16 × 9 × 1 (0.1) 2 h = 14400 c m

.
Therefore, the correct option is 1.

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