Answer
$\dfrac{27}{8}$
Work Step by Step
$\iiint_E z dV= \int_{0}^{ \pi/2}\int_0^3 \int_0^{1/3} z dx r dr d\theta$
$=\int_{0}^{ \pi/2}\int_0^3 z [x]_0^{(1/3)} r dr d\theta$
$=(\dfrac{1}{3}) \int_{0}^{ \pi/2}\int_0^3 r \sin \theta[ r \cos \theta]r dr d\theta$
$=\dfrac{1}{12} \int_{0}^{ \pi/2}[r^4]_0^3 \sin \theta \cos \theta d\theta$
$=\dfrac{1}{12} \int_{0}^{ \pi/2}[(3-0)^4] \sin \theta \cos \theta d\theta$
$=\dfrac{81}{12} \int_{0}^{ \pi/2} \sin \theta \cos \theta d\theta$
$=\dfrac{27}{8}$
