z>=0 and (h - z) cos(ϕ) + z<=(h x)/R and x^2 + y^2<=R^2

h

S_L = (2 h R (sin(ϕ) - ϕ cos(ϕ)))/(1 - cos(ϕ))

x^_ = (-(R (-5 cos(ϕ) sin(ϕ) + 2 cos^3(ϕ) sin(ϕ) + 3 ϕ))/(4 (-2 sin(ϕ) - cos^2(ϕ) sin(ϕ) + 3 cos(ϕ) ϕ)), 0, (h (-13 cos(ϕ) sin(ϕ) - 2 cos^3(ϕ) sin(ϕ) + 3 ϕ + 12 cos^2(ϕ) ϕ))/(8 (-1 + cos(ϕ)) (-2 sin(ϕ) - cos^2(ϕ) sin(ϕ) + 3 cos(ϕ) ϕ)))

V = (h R^2 (3 sin(ϕ) - 3 ϕ cos(ϕ) - sin^3(ϕ)))/(3 (1 - cos(ϕ)))

convex solids | ungulae