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We have a solid lead ball of radius 6 cm. It needs to be melted and then drawn into a wire of diameter 0.2 cm. How much long wire can be produced from the given ball?

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272 m

288 m

292 m

296 m

answer is B.

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Detailed Solution

We have given a solid lead ball of radius 6 cm.
We know that the volume of a sphere V =

43 π r 3,

where r is the radius of the sphere.
Volume of a cylinder is

π r 2 h,

where r is the radius of the cylinder and h is the height of the cylinder.
Since the radius of the solid ball is 6 cm, therefore we can calculate the volume of the solid ball as shown,

V = 43 π r 3 = 43 π × 63 = 288 π cm 3

Let the length of the wire be h cm.
Since the diameter of the wire is 0.2 cm, so radius of the wire will be,

r 1 = 0.2 2 = 0.1 cm

.
The volume of the wire,

V 1 = π r 1 2 h .

Since the wire is drawn into a solid lead ball, we can calculate length of the wire as shown,

288 π = π 0.1 2 h ⇒ h = 28800 cm ⇒ h = 288 m              [∵ 1m = 100cm]

So, 288 m long wire can be produced from the given ball.
Therefore, the correct answer is option (2).

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