why nuclear radius is considered till that point where the nuclear density becomes half?

The density of the nucleus is ver high ( of the order of 10¹⁷ ) while that of the atom is very small . This is due to the fact that the atom contains a lot of empty space , hence nuclear radius is considered till the point where the nuclear density becomes half.

'Metre', no doubt is the SI unit of distance, but for smaller distances like the radius of nucleus , we calculate it in fermi ( 1 fermi = 10^-15 m ) or angstrom ( 1 A^o = 10^-8 m ).

Also, pls. let us know where you are getting stuck on this question, once we are clear, we would be able to explain things better.