Question

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

Answer 1

The radius of copper sphere, `R = 18/2`= 9 cm

The volume of sphere `= 4/3 pi xx (9)^3`

`= 4/3 pi xx 729`

`= 972 pi cm^2`

Since,

The sphere is melted and drawn into a long circular wire of length 108 m = 10800 cm

Let r be the radius of wire,

Clearly,

The volume of wire = volume of sphere

`pi xx r^2 xx 10800 = 972 pi`

`r^2 = (972)/(10800)`

   ` =9/100`

`r = 3/10`

`r = 0.3 cm`

And, d = 2r = 0.6 cm

Hence, the diameter of the wire will be equals to 0.6 cm