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

  1. Chapter 13 Class 10 Surface Areas and Volumes
  2. Serial order wise
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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 = ๐œ‹๐‘Ÿ2โ„Ž = ฯ€ร—(1/2)^2ร—8 = ฯ€ร— 1/4 ร— 8 = 2๐œ‹ cm3 Volume of wire Wire is form of cylinder with radius = r length = height = h = 18 m = 18 ร— 100 = 1800 cm Volume of wire = ๐œ‹๐‘Ÿ2โ„Ž = ๐œ‹๐‘Ÿ2ร—1800 = 1800๐œ‹๐‘Ÿ2 cm2 Now, Volume of copper rod = Volume of wire 1800๐œ‹๐‘Ÿ2=2๐œ‹ 1800๐‘Ÿ2=2 r2 = 2/1800 r2 = 2/1800 r2 = 1/900 r = โˆš(1/900) r = โˆš(1/(30 ร— 30)) r = โˆš(1/ใ€–30ใ€—^2 ) r = 1/30 So, r = 1/30 cm โˆด Thickness of wire = Diameter of wire = 2r = 2 ร—1/30 = 1/15 cm

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