The diameter of a copper shere is 6 cm. The sphere is melted and drawn into a long wire of niform circular cross section. If the length fo the wire is 36 m, find its thickness.

Answer

`2 mm`

Explanation

Radius of the sphere, R = 3 cm.
Volume of the sphere `= 4/3piR^(3)`
`=(4/3pixx3xx3xx3)cm^(3)`
`=(36pi)cm^(3)`.
Length of the wire, h = 36 m = 3600 cm.
Let the radius fo the wire be r.
`"Volume of the wire "pir^(2)h=(pir^(2)xx3600) cm^(3)`.
But, volume of the wire = volume of the sphere
`rArr" "3600pir^(2)=36pirArrr^(2)=1/100`
`rArr" "r=sqrt(1/100)cm=1/10=1mm.`
Hence, thickness of the wire = its diameter = 2 mm.