TITLE: What is the volume of this 3d shape?
QUESTION [5 upvotes]: I'm wondering if there is an equation that represents the volume of an arbitrary 3d primitive
matching this description:
1.) Point at center of sphere
2.) Each edge is the length of the radius
3.) 3 flat sides, 1 arc side
Image: 

So it's kind of a sector of a sphere, but instead of a conical shape it's more of a tetrahedral shape, but with a curved end.

REPLY [2 votes]: The volume is $\frac13\Omega r^3$, where $\Omega$ is the solid angle subtended at the centre. Wikipedia has several formulas for the solid angle, including the one in Rahul's answer.