# How Much Radius of Wire in an Iron Sphere ?

An iron sphere of radius 27 cm is melted to from a wire of length 729 cm. The radius of wire is

- 6 cm
- 9 cm
- 18 cm
- 36 cm

**Answer: (1) 6 cm**

**Explanation:-**

The radius of an iron sphere = 27 cm

**Formula-**

**The volume of an iron sphere = 4 x pai x r ^{3}/3**

**Where, r = the radius of a sphere.**

Then, the volume of a sphere = 4 x 22 x 27

^{3}/7 x 3cm

^{3}

**Formula-**

**The volume of the wire = pai x r**

^{2}x h**where, r = radius of the wire & h = the length of the wire.**

Then, the volume of the wire = 4 x 22 x 27

^{3}/7 x 3 = pai x r

^{2}x 729

4 x 22 x 27 x 27 x 27/7 x 3 = 22 x r

^{2}x 729/7

4 x 9 x 27 x 27 = r

^{2}x 729

4 x 9 = r

^{2}

36 = r

^{2}

r = 6 cm (square root of both side)

Hence, the radius of the wire is 6 cm.