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Question

A solid lead ball of radius 6 cm is melted and then drawn into a wire of diameter 0.2 cm. The length of wire is

(a) 272 m (b) 288 m (c) 292 m (d) 296 m

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Solution

ANSWER:
(b) 288 m
From question,
Radius of lead ball =6 cm
Diameter of wire =0.1 cm
So, radius of wire =0.2 cm2=0.1 cm
Let h metre be the length of wire.
Volume of the lead ball = volume of the wire
43πr3=πr2h
43π×63=π×0.12h
43×216=0.01h
4×72=0.01h
h=4×720.01 cm
h=2880.01 cm
h=2880.01×1100 m[1 cm=1100 m]
h=2880.01×100 m
h=288 m
Therefore, the length of the wire is 288 m.


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