Answer
$\dfrac{1}{2}\pi kha^4$
Work Step by Step
Consider $I_z=\iiint_{E} (x^2+y^2) \rho(x,y,z) dV$
or, $=k\int_{0}^{2 \pi} \int_{0}^{h}\int_{0}^{a}(r^2)r dr dz d\theta $
or, $=k\int_{0}^{2 \pi} \int_{0}^{h}\int_{0}^{a}(r^3) dr dz d\theta $
or, $=k \int_{0}^{2 \pi} d\theta \int_{0}^{h} dz \int_{0}^{a}(r^3) dr $
or, $=2\pi k [z]_0^h [\dfrac{r^4}{4}]_0^a $
or, $=2\pi k (h-0) [\dfrac{a^4}{4}-0] $
or, $I_z=\dfrac{1}{2}\pi kha^4$
