Question

If the radius of a wire is decreased to one third, if the volume is same, then find the length of the wire (in times).​

Answer 1

Answer

Length becomes 9 times

Explanation

Volume = area of cross section × length of wire

Let the original length of wire be l and original radius be r.

Area of cross section (assuming the wire is cylindrical having a circular cross sectional area) = πr²

thus, volume = πr² × l

= lπr²

Now, the radius is made 1/3 times. This means new radius = r/3. Let the new length be l'

Volume of new wire = π(r/3)² × l'

= l'πr²/9

Now since both volume is same, we will equate them

⇒ lπr² = l'πr²/9

⇒ l = l'/9

⇒ l' = 9l

This means that new length is 9 times the original.