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

1. 0.5 cm

2. 1 cm

3. 1.2 cm

4. 1.5 cm

Given,

Let the wire's radius be a.

Given, sphere is melted into the wire.

The wire formed is a cylinder, hence the volume of wire will be equal to the volume of sphere.

Radius of sphere, r = $\dfrac{\text{diameter}}{2} = \dfrac{6}{2}$ = 3 cm

Volume of sphere, V = $\dfrac{4}{3} π\text{r}^3$

$= \dfrac{4}{3}π \times 3^3 \\[1em] = \dfrac{4}{3}π \times 27 \\[1em] = 4 \times 9π \\[1em] = 36 π \text{ cm}^3$

Given, length of wire = 36 cm

So, height of cylinder = 36 cm

Volume of cylinder, V = 36 π cm³

∴ πr²h = 36 π

$\Rightarrow \text{r}^2 \times 36 = 36 \\[1em] \Rightarrow \text{r}^2 = \dfrac{36}{36} \\[1em] \Rightarrow \text{r}^2 = 1 \\[1em] \Rightarrow \text{r} = \sqrt{1} \\[1em] \Rightarrow \text{r} = 1 \text{ cm.}$

Hence, option 2 is the correct option.