A metallic cylindrical rod is melted and recasted as a rod which has one-fourth of the radius of the original rod. Its length will be

16 times

Let the radius of the rod = r

We know that the volume of the rod = πr²h

and the radius of the new rod = r/4

So the volume of the new rod = π(r/4)²H

πr²h : π(r/4)²h

π(r)²h : πr²/16H

here, h/H = 1/16

So, its length will be 16 times.