Let $a_{r},\:a_{\phi }$ and $a_{z}$ be unit vectors along $r,\:\phi$ and $z$ directions, respectively in the cylindrical coordinate system. For the electric flux density given by $D=\left ( a_{r}15+a_{\phi } 2r - a_{z} 3rz \right ) \text{ Coulomb}/m^{2}$, the total electric flux, in Coulomb, emanating from the volume enclosed by a solid cylinder of radius $3\:m$ and height $5\:m$ oriented along the $z$-axis with its base at the origin is:
- $54\:\pi$
- $90\:\pi$
- $108\:\pi$
- $180\:\pi$