Obtain the volume of the solid which is bounded by a circular paraboloid z=x^2+y^2, cylinder x^2+y^2=4, and Coordinate plane. And the solid is in the (x>=0, y>=0, z>=0).

Cylindrical coordinates can be given as,
${\displaystyle x=r\cos \theta }$
${\displaystyle y=r\sin \theta }$
${\displaystyle z=z}$
${\displaystyle x^2+y^2=r^2}$
Now the r will be 2 as ${\displaystyle x^2+y2=2^2}$. Limits of region can be given as,
${\displaystyle R\{(r,\theta ,z):0\le r\le 2,0\le \theta \le \frac{\pi }{2},0\le z\le r^2\}}$
Volume of solid in cylindrical coordinate plane is given as,
${\displaystyle V={\oint }_{R}rdrd\theta dz}$
Calculate the volume using the values,
${\displaystyle V={\int }_0^{\frac{\pi }{2}}{\int }_0^2{\int }_0^{r^2}rdzdrd\theta }$
${\displaystyle ={\int }_0^{\frac{\pi }{2}}{\int }_0^{2}r{\left[z\right]}_0^{r^2}drd\theta }$
${\displaystyle ={\int }_0^{\frac{\pi }{2}}{\int }_0^2{r}^{3}drd\theta }$
${\displaystyle ={\int }_0^{\frac{\pi }{2}}{\int }_0^2{\left[\frac{r^4}{4}\right]}_0^{2}d\theta }$
${\displaystyle ={\int }_0^{\frac{\pi }{2}}4d\theta }$
${\displaystyle =4{\left[t\hat{e}\right]}_0^{\frac{\pi }{2}}}$
${\displaystyle =4[\frac{\pi }{2}-0]}$
${\displaystyle =2\pi }$
Volume of the given solid is ${\displaystyle 2\pi }$