Question

The diameter of a copper sphere is 6 cm. it is melted and drawn into a long wire of uniform circular cross section. if the length of the wire is 36 cm , then find the radius.

Answer 1

$volume \: of \: sphere = volume \: of \: wire \\ \frac{4}{3} \pi {( \frac{6}{2} )}^{3} = \pi {r}^{2} \times 36 \\ \frac{4}{3} \times 3 \times 3 \times 3 = {r}^{2} \times 36 \\ {r}^{2} = \frac{4 \times 3 \times 3}{36} = 1 \\ r = 1cm$

Answer 2

Given:

The diameter of a copper sphere is 6 cm. It is melted and drawn into a long wire of uniform circular cross-section. Also, the length of the wire is 36 cm.

To find:

The radius of the wire.

Solution:

The radius of the wire is 1 cm.

To answer this question, we will follow the following steps:

As given, we have,

The diameter of copper sphere = 6cm

So,

The radius of copper sphere = 6/2 = 3cm

Also given,

The length of wire = 36 cm

Now,

As given, the copper sphere is melted to make a long wire of uniform cross-section, so the volume of the copper sphere and wire will be equal.

The volume of a copper sphere

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

The volume of wire, which is in the form of a cylinder

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

So,

$\frac{4}{3} \pi \: {r}^{3} = \pi \: {r }^{2} \: h$

On putting the values, we get

$\frac{4}{3} \times {(3)}^{3} = {r}^{2} \: 36$

( pi will get cancelled)

On solving the above, we get

${r}^{2} = 1$

Taking square root on both sides, we get,

$r = 1 \: cm$

Hence, the radius of the wire is 1 cm.