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A piece of ductile metal is in the form of cylinder of diameter. 1cm and length 11cm . It is drawn out into. A wire of. Diameter1mm . What will be the length. Of the wire so obtained? |
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Answer» VOLUME of the metal CYLINDER = π r2h Here r = 1/2cm, h= 11cm Volume = π(1/2)211 = π*1/4*11 = 11π/4 cubic cm. The diameter of the wire = 1mm. radius = Diameter/2 = 1/2 mm. 1cm = 10 mm so 1/2mm = 1/20cm. or Radius = 1/20 cm. Convert the radius of the wire into cm as we have calculated the volume of the cylinder in cubic cm. If we change the SHAPE of a solid, its volume doesnt change so the volume of the wire would be EQUAL to the volume of the cylinder. The wire is also in shape of a cylinder. Let the length or height of the wire be x cm. The volume of the wire = π r2h = π (1/20)2 x = π *1/400*x But as we have discussed this volume of the wire should be equal to the volume of the cylinder. So π *1/400*x = 11π/4 so x = (11*400*π)/π*4 or x = 1100 cm. So the length of the wire = 1100CM. |
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