[ot][ot][ot][personal] whirligig small thoughts

[Undescribed Horrific Abuse, One Victim & Survivor of Many]

a wedge made of a stack of triangles, each one with area of 1/2 r^2 dtheta
where r is the radius of a sphere slice
uhh so that's really sqrt(r^2 - x) where x runs from -r to +r

two different r's here let's subscript them
a wedge made of a stack of triangles
each one with area of 1/2 r_slice^2 dtheta
now,
r_slice^2 + height^2 = r_sphere^2
so if we run x=height from -r to r
r_slice = sqrt(r_sphere^2 - x^2)

then maybe plug in to other expression

dvolume = 1/2 sqrt(r_sphere^2 - x^2)^2 dtheta
dvolume = 1/2(r_sphere^2 - x^2) dtheta

maybe unsure