Find the volume of the solid that lies within the sphere $^2+^2+^2=81$, above the plane, and outside the cone $=5\sqrt{^2+^2})$.

My difficulties are that having it be outside the cone, you must also have a way to find the volume of the tip of the sphere over the cone. I tried to represent the tip by looking at the xz plane shown in the picture below. I see no way to express this spherically or cylindrically. My best bet is to calculate the hemisphere volume by $\frac43\pi r^3$ and then subtract the cone volume from that which is found rather easily cylindrically.

Thank you.

[![enter image description here](https://i.stack.imgur.com/bmoWi.png)](https://i.stack.imgur.com/bmoWi.png)