Question

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

Answer 1

It is given in the question that, 

Diameter of the wire = 1cm 

Hence, 

Radius of the wire = 0.5 cm 

Length or the height of the wire = 11 cm 

Hence, 

The volume of the wire = \(\pi r^2h\)

= \(\frac{22}{7}\times0.5\times0.5\times11\)

= 8.643 cm³

Now, 

We know that, 

The volumes of both the cylinders would be the same. 

And, 

Diameter of the new wire = 1mm = 0.1 cm 

Radius = 0.05 cm 

Therefore the new length of the wire would be = \(\frac{volume}{\pi r^3}\)

= \(\frac{8.643\times7}{22\times0.05\times0.05}\)

= 1100.02 cm 

= 11 m