A positively charged solid nonconducting cylinder of length \(\ell=10 \mathrm{~m}\) and radius \(R=50 \mathrm{~mm}\) has uniform volume charge density \(+9.0 \times 10^{-9} \mathrm{C} / \mathrm{m}^{3}\).

(a) What is the charge inside the cylinder? Avoiding the regions near the ends, determine the electric field magnitude at

(b) \(r=40 \mathrm{~mm}\) and 

(c) r=60 mm, where r is the radial distance from the long central axis of the cylinder.