Question

The diameter of a coper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.

Answer 1

In the given problem, the first step is to find the volume of the sphere.

Here,

The diameter of the sphere = 18 cm

So, the radius of the sphere =

Therefore, the volume of the sphere =

Now, the sphere is melted and drawn into a long wire of uniform cross section. So, the volume of both the sphere and the wire will be equal.

For the wire,

Length of the wire = 108 m

= 10800 cm

Let the radius of the wire = x cm

So the volume of the wire =

According to the question,

So, the radius of the wire is 0.3 cm.

Therefore, the diameter of the wire is