Question

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

Answer 1

In the given problem, we are given a sphere which is melted and drawn into a wire. So, here, the first step is to find the volume of the sphere.

Here,

The diameter of the sphere = 6 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,

Diameter of the wire = 0.2 cm

Radius of the wire = 0.1 cm

Let the length of the wire = x cm

So, the volume of the wire =

Now, volume of sphere = volume of wire,

So, the length of the wire is