Question

A solid sphere if diameter 2 cm is melted to droma wire of length 1 meter. Thr radius of the wire

Answer 1

Question :

A solid sphere of diameter 2 cm is melted and drawn into a wire of length 1 meter. The radius of the wire is?

Solution :

When an object is melted, and recast into different shape, The volume of the object remains unchanged.

Given, Diameter of solid sphere = 2 cm

Radium of solid sphere = 1 cm.

Volume of a sphere with radius r is given by,

$V = \frac{4}{3} \pi {r}^{3}$

Now, r = 1 cm

$V = \frac{4}{3} \pi {r}^{3} \\ \\V = \frac{4}{3} \pi ({1}^{3}) \\ \\ V = \frac{4}{3} \pi$

Now, The solid sphere is melt and drawn into a wire.

The wire has the shape of cylinder.

Let the radius of wire be r.

Given, length of the wire = 1m = 100 cm.

Volume of a cylinder with height h, radius r is given by,

$v = \pi \: {r}^{2} h$

Now

Volume of the wire = Volume of the sphere

$v = \frac{4}{3} \pi = \pi( {r}^{2} )h \\ \frac{4}{3} = {r}^{2} \times 100 \\ \\ {r}^{2} = \frac{4}{100 \times 3} \\ \\ {r}^{2} = \frac{1}{25 \times 3} \\ \\ r = \frac{1}{2} \times \frac{1}{ \sqrt{3} } = \frac{1}{2} \times \frac{ \sqrt{3} }{3} = \frac{ \sqrt{3} }{6}$

Therefore, Radius of the wire is

$\frac{ \sqrt{3} }{6} cm$