Find the volume of the region in the first octant underneath the paraboloid $$z = 1 - \frac{x^2}{81} - \frac{y^2}{36}$$
I've been given the hint to use the change of variables $x = 9rcos(\theta)$ and $y = 6rsin(\theta)$
I know that $x > 0, y > 0, z > 0$ since we're in the first octant. Still not quite sure how to go about finding the limits, and how to use the substitution.
HINT
draw the region by plot on $x-y$, $z-x$, $z-y$ plane and find the limit of integration
set up the integral in cartesian coordinates $\iiint_V 1 dxdydz$
set up the integral in polar coordinates $\int_0^{\frac{\pi}2}\int_0^{1}\int_0^{r(z)} |J| dr\,dz\,d\theta$