Answer
$379 $
Work Step by Step
To find how many turns of wire are needed, we first need to find the length of this wire.
We know that the resistance is given by
$$R=\dfrac{\rho L}{A} $$
Hence, the length of the wire is given by
$$L_{\rm wire}= \dfrac{RA }{\rho_{\rm aluminum}}\tag 1$$
This length $L$ will make too many turns where the length of one turn is given by the circumference of one turn $$L_{\rm turn}=2\pi r_{\rm turn}\tag 2$$
Hence, the number of turns is given by
$$N=\dfrac{L_{\rm wire}}{L_{\rm turn}}$$
Plug from (1) and (2);
$$N=\dfrac{RA }{2\pi r_{\rm turn}\rho_{\rm aluminum}}$$
Plug the known;
$$N=\dfrac{(1000)(10\times 10^{-6}\times 10\times 10^{-6})}{2\pi (1.5\times 10^{-3}) (2.8\times 10^{-8})}$$
$$N=\color{red}{\bf 379}\;\rm turn$$
