I have to find the volume between the cone $x=\sqrt{y^2+z^2}$ and the sphere $x^2+y^2+z^2=81$
So I first set up $x=0$ to find the bounds for $\rho$ and $\phi$.
When I do that I get a circle on the $yz$ plane with radius 9.
So I have $0 \le \rho \le 9$ and $0 \le \phi \le \pi$
Then I set $z=0$ to find bounds for $\theta$ and I get a circle with radius 9 and the lines $y=|x|$.
So I have the bounds be $0 \le \theta \le \pi/4$.
$$ \int^{\pi/4}_0\int^{\pi}_0\int^9_0 \rho^2sin{\phi}\; d\rho\,d\phi\,d\theta $$
The answer is wrong though, does anyone know where I went wrong in my work?