A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be `8. 88g"\ "p e r"\

Explanation

Diameter of the wire = 3 mm = 0.3 cm.
Length of the cylinder = 12 cm.
Radius fo the cylinder = 5 cm.
`"Number of turns"=("length of the cylinder")/("diameter of the wire")=12/0.3=40.`
Length of one ture = circumference of the base of the cylinder
`=(2xx3.14xx5) cm = 31.4 cm`.
`"Length of 40 turns"=(31.4xx40) cm=1256 cm.`
`"Total length of the wire wrapped, l = 1256 cm"`
`"Radius of the wire. "r=(0.3/2)cm=0.15 cm.`
`"Volume of the wire "=pir^(2)l=(3.14xx0.15xx0.15xx1256) cm^(3)`
`=88.7364 cm^(3)~~88.74 cm^(3)`.
`:." mass of hte wire = volume "xx"dendsity = "(88.74xx88.8) g`
`=788.01 g ~~788g("approx.")`