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Example 10 - A copper rod of diameter 1 cm, length 8 cm - Conversion of one shape to another

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Example 10 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. Volume of copper rod = Volume of wire Volume of copper rod Copper rod is in form of cylinder with Diameter of rod = 1 cm So, radius = r = 1/2 cm And, length = height = h = 8 cm Volume of copper rod = 2 = (1/2)^2 8 = 1/4 8 = 2 cm3 Volume of wire Wire is form of cylinder with radius = r length = height = h = 18 m = 18 100 = 1800 cm Volume of wire = 2 = 2 1800 = 1800 2 cm2 Now, Volume of copper rod = Volume of wire 1800 2=2 1800 2=2 r2 = 2/1800 r2 = 2/1800 r2 = 1/900 r = (1/900) r = (1/(30 30)) r = (1/ 30 ^2 ) r = 1/30 So, r = 1/30 cm Thickness of wire = Diameter of wire = 2r = 2 1/30 = 1/15 cm

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.