A piece of ductile metal is in the form of a cylinder of diameter 1 cm

1.	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» 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

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»

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