$\text{Let x is the length of the wire, then length of solenoid is}$

$ x = 2\pi rN$

$ N = \frac{x}{2\pi r}$

$\text{Area of cross section} A = \pi r^2$

$\text{Self Inductance} L = \frac{\mu_0 N^2A}{l}$

$\Rightarrow L = \frac{\mu_0 \pi r^2 \frac{x^2}{(2\pi r)^2}}{l}$

$\Rightarrow x = \sqrt{\frac{4\pi Ll}{\mu_0}}$