Question

The diameter of a iron sphere is 8 cm. It is beaten and drawn into a wire with a diameter of 2 mm. Find the length of the wire.

Answer 1

Answer : The length of the wire is, 8533 cm

Step-by-step explanation :

As the iron sphere is beaten and drawn into a wire. That means, their volume will be equal.

Volume of iron sphere = Volume of cylindrical wire

The formula will be:

`(4)/(3)\pi r_1^3=\pi r_2^2h`

where,

`r_1` = radius of sphere =
`(Diamtere)/(2)=(8cm)/(2)=4cm`

`r_2` = radius of cylindrical wire =
`(Diamtere)/(2)=(2mm)/(2)=1mm=0.1cm`

h = height of cylindrical wire or length of wire

Now put all the given values in the above formula, we get:

`(4)/(3)\pi r_1^3=\pi r_2^2h`

`(4)/(3)* r_1^3=r_2^2h`

`(4)/(3)* (4)^3=(0.1)^2h`

`h=8533.33cm\approx 8533cm`

Therefore, the length of the wire is, 8533 cm