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.

Explanation

Diameter of copper sphere `D=18 cm`
Length of wire `l=108 m=10800 cm`
Radius of copper sphere,` R=D/2 =9 cm`
Volume of copper sphere `V=4/3piR^3`
`=>4/3pi(9)^3`
`=4/3pixx729=972picm^3`
The sphere is melted and is drawn in a wire (cylindrical) of radius (r) and hight 108 m.
Volume of sphere = Volume of wire
Volume of wire `V=pir^2l`
`=>972picm^3=pir^2l`
`r^2=972/10800cm^3`
`r^2=.09cm^2`
`r=.3 cm`
Diameter of the wire `d=2r=0.6 cm`