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

Diameter of sphere = 42 cm

Radius of sphere = 21 cm

Volume of sphere `= 4/3pir^3 = 4/3pixx21xx21xx21 "cm"^3`

Diameter of wire = 2.8 cm

Radius of wire =1.4 cm

Let the length of the wire be / cm.

The volume of the sphere is equal to the volume of the wire therefore,

`pixx1.4xx1.4xxl = 4/3pixx21xx21xx21`

`l =(4xx21xx21xx21)/(3xx1.4xx1.4) = 6300 "cm" = 63   "m"`

So, the wire is 63 m long.