Question

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.

Answer 1

Radius of the sphere `=42/2 = 21 "cm"`

volume of sphere`=4/3pi"r"^3`

`=(4/3pixx21xx21xx21) "cm"^3`

Radius of the wire `=2.8/2 = 1.4 "cm" ` 

Let the length of the wire be h cm. then, 

Volume of the wire= πr²h

`=(pixx14/10xx14/10xx"h")"cm^3"`

Therefore

`4/3 pixx21xx21xx21=pixx14/10xx14/10`

`=>12348=(49/25)xx"h"`

`=> "h" = 6300 "cm"`

`=> "h" =(6300/100) "m"`

⇒ h = 63 m

Hence, the length of the wire is 63 m.