A cylindrical rod of length L and radius r, made of an inhomogeneous dielectric, is placed with its axis along the Z-direction with one end at the origin as shown below. If the rod carries a polarization P = ( 5z^2 + 7 ) k, the volume bound charge inside the dielectric is

A cylindrical rod of length L and radius r, made of an inhomogeneous dielectric, is placed with its axis along the Z-direction with one end at the origin as shown below.

If the rod carries a polarization $$\overrightarrow{\mathbf{P}}=\left(5z^2+7\right)\hat{\mathbf{k}},$$    the volume bound charge inside the dielectric is

Answer: Option D