c
Suppose solenoid has \(N\) turns, each of radius \(r\) and length of wire is \(l.\)

\(L = \frac{{{\mu _0}{N^2}A}}{{{l_0}}} = \frac{{{\mu _0}{N^2}\pi {r^2}}}{{{l_0}}}\) .... \((i)\)

\(l = N \times 2\pi r\) \( \Rightarrow {N^2}{r^2} = \frac{{{l^2}}}{{4{\pi ^2}}}\) .... \((ii)\)

\(l = \sqrt {\frac{{4\pi L{l_o}}}{{{\mu _o}}}} \)