A copper rod of diameter 1 centimetres and length 8 centimetres is drawn into a wire of length 18 metre of uniform thickness. find the thick ness of the wire.
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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
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
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