it gets confusing as i approach the sphere, maybe involves more things held in short term memory
so the way i'm trying to figure the volume of a sphere is by integrating wedges. since the wedges will be dtheta, we can assume their outer surfaces are flat, and approximate them with triangles again. the approach i've been trying to consider is to think of a wedge as a semicircle (known volume) where the thickness at each point is proportional to the distance from the semicircle axis. then i was
