1 Aug
2023
1 Aug
'23
9:19 p.m.
wedge_volume = integral(triangle_area, x=-r_sphere..+r_sphere) triangle_area = 1/2 r_slice^2 dtheta r_slice = sqrt(r_sphere^2 - x^2) wedge_volume = I{-r_sphere..+ triangle_area dx wedge_volume = I{-r_sphere..+ 1/2 r_slice^2 dtheta dx wedge_volume = I{-r_sphere..+ 1/2 sqrt(r_sphere^2 - x^2)^2 dtheta dx wedge_volume = I{-r_sphere..+ 1/2 (r_sphere^2 - x^2) dtheta dx wedge_volume = dtheta/2 I{-r_sphere..+ (r_sphere^2 - x^2) dx next step: integrate (r_sphere^2 - x^2) dx