Question

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Answer 1

Given diameter of copper rod, d = 1 cm
Hence its radius, R= (1/2) cm
Height of rod, H = length of rod = 8 cm
∴ Volume of rod = πR²H cubic units
= π x (1/2)² x 8 cubic cm
= 2π cubic cm
Given that cylindrical rod is drawn into a cylindrical wire of length, h = 18 m
That is, h = 1800 cm
∴ Volume of cylindrical rod = Volume of cylindrical wire
Let r be the radius of the wire
Hence 2π = πr²h
That is, 2 = r² x 1800
r² = (1/900)
Therefore, r = (1/30) cm = 1/3 mm
Diameter or thickness = 2(1/3) = (2/3) mm