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

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20m

30m

44m

36m

answer is D.

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Detailed Solution

Given that the diameter of a sphere is

6 cm

and the diameter of the wire is 2mm.
We have the following formula,
Volume of sphere =

43 × π × r 3

Volume of cylinder =

π × r 2 × h

Radius of the sphere will be 3cm.
The volume of the sphere will be,

43 × π × 33

4 × 9 × π

36 π c m 3

Radius of the wire will be,

2 mm 2 = 1 m m = 0.1 c m

10mm=1cm
Volume of wire will be,
=

π × 0.1 × 0.1 × h

0.01 π h c m 3

Volume of sphere = Volume of wire

36 π = 0.01 π h

h = 36 0.01

h = 3600 cm
h = 36 m 1m=100cm
Thus the length of the wire is 36 m.
Therefore the correct option is 4.

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