A positively charged nonconducting solid sphere of radius \(R\) has a nonuniform volume charge density given by \(ho_{0}\) for \(r \leq R / 2\) and given by \(2 ho_{0}(1-r / R)\) for \(R / 2 \leq r \leq R\), where \(r\) is the radial distance from the sphere center.

(a) Determine the charge \(q\) on the sphere in terms of \(ho_{0}\) and \(R\).

(b) Determine \(E\) in terms of \(ho_{0}, r\), and \(R\).

(c) Show that the electric field is continuous at the boundaries.