Question

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?

Answer 1

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.