Answer
$470\space turns$
Work Step by Step
We can find the number of turns as follows:
$N=\sqrt{\frac{lL}{\mu_{\circ}A}}$
We plug in the known values to obtain:
$N=\sqrt{\frac{(0.22)(45\times 10^{-3})}{(4\pi\times 10^{-7})(0.035)}}$
$N=470\space turns$
