Question

A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width.

Answer 1

We have,

Radius of the metallic sphere, R `= 8/2 = 4  "cm"` and

Height of the cylindrical wire, h = 12 m = 1200 cm

Let the radius of the base be r.

Now, 

Volume of the cylindrical wire = Volume of the metallic sphere

`=> pi"r"^2"h" = 4/3 pi"R"^3`

`=> "r"^2 = (4"R"^3)/(3"h")`

`=> "r"^2 = (4xx4xx4xx4)/(3xx1200)`

`=> "r"^2 = 16/225`

`=> "r" =sqrt(16/225)`

`=> "r" = 4/15  "cm"`

∴ The width of the wire = 2r

`=2xx4/15`

`=8/15 "cm"`

So, the width of the wire is `8/15` cm.