The resistance of a wire is given by:

R = p*L / A (*where p=resistivity of material, L=length, A=area, R=resistance)

rearranging the equation we can solve for L,

L = (R*A) / p

we are given R = 4.3 Ω

A = area of circle = pi*r^2 ,

r = radius = diameter / 2 = 0.5 / 2 mm = (0.5 / 2 )*10^-3 m = 0.25*10^-3 m

so A = pi*(0.25*10^-3 m)^2

and p = resisitivity of copper, which is 1.7*10^-8 Ω*m

(for a list of resisitivity of materials refer to this link: http://answermenu.com/?qa=325/platinum-copper-equal-length-found-resistance-ratio-radii

plugging into formula above we can solve for L:

L = ( (4.3 Ω)*(pi*(0.25*10^-3 m)^2 )) / (1.7*10^-8 Ω*m )

L = 49.7 m

The total number of turns on the solenoid is given by:

N = L / (2pi*r)

plugging in our numbers we get:

r = 1 cm = 1*10^-2 m

N =49.7 m / (2pi*(1*10^-2 m)) = 790 turns