Question

The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross-section. If the length of the wire is 108 m, find its diameter.

Answer 1

Diameter of sphere = 18 cm
Radius of the sphere = 9 cm

Volume of sphere`=4/3 pir^3 = 4/3pixx9xx9xx9  "cm"^3`

Length of wire = 108 m = 10800 cm

Let radius of the wire be r cm.

Volume of the wire` = pir^2l = pixxr^2xx10800   "cm"^3`

The Volume of the sphere and the wire are the same.

Therefore,

`pixxr^2xx10800 = 4/3pixx9xx9xx9`

`rArr r^2 =(4xx9xx9xx9)/(3xx10800) = (4xx9xx9)/(3xx4xx3) =0.9 `

`rArr r^2 =sqrt(0.09) = 0.3  "cm"`

Thus, d=2r =2 ×0.3 cm = 0.6 cm

The diameter of the wire is 0.6 cm.