In a Newton's rings experiment, the radius of ring of the lens is 10.0cm and its diameter is 5.0cm. Determine how many of that rings are produced

I am not certain of what you mean radius and diameter. I think you can use

xm = [(m + ½)λR]½

but I don't know what you mean.
http://www.fas.harvard.edu/~scdiroff/lds/LightOptics/NewtonsRings/NewtonsRings.html