Abstract definition of a cone: locus of points of line segments join a single point $v$, called vertex with set of coplanar points called base.
Height of cone is distance from vertex to plane.
If I take strange set of co-planer point such as complicated design for example, as base then volume of the set join with some vertex is still given : $\tfrac13$ (base)(height).
How can I prove this in calculus?
I have tried a few it is too late to wake my sister, thank you.