Understanding an issue in a triple integral solution Here I have a triple integral $$ \iiint f(x,y,z)dxdydz $$ on the region : $\\{\sqrt[]{x^2+y^2} \le z \le \sqrt[]{4-x^2-y^2}\\} $ if we use cylindrical coordinates we have : **(1)** $ r\le z \le \sqrt[]{4-r^2} $ and when we want to do the integral : we determine that : $ 0 \le \theta \le 2\pi $ $ $ , $ $ $ 0 \le r \le \sqrt{2}$ my problem is the **z** according the graph **z** is bigger than the Cone so it should be : between $0 \le z \le \sqrt{4-r^2}$ **but** according to equation I determine that z is between : $r \le z \le \sqrt{4-r^2}$ what I'm missing here ?

Here is the cross section of the integration volume in $r-z$ plane:

!Here is the cross section in $r-z$ plane

The integration of the volume $D$ is given by (assuming that $f(x,y,z)=F(z,r)$): $$\int_D f(x,y,z)dxdydz=\int_0^{2\pi}d\theta \int_0^{\sqrt{2}} rdr \int_{r}^{\sqrt{4-r^2}}dz F(z,r)$$