V = π a^2 h (volume enclosed by capping the surface above and below assuming height h, radius a)

x(u, v) = a cos(u) y(u, v) = a sin(u) z(u, v) = v

x^2 + y^2 = a^2 and 0<=z<=h

2

S = 2 π a h

ds^2 = 1 du^2 + a^2 dv^2

dA = a du dv

x^_ = (0, 0, h/2)

I = (1/12 (3 a^2 + 4 h^2) | 0 | 0 0 | 1/12 (3 a^2 + 4 h^2) | 0 0 | 0 | a^2/2)

K(u, v) = 0

(for a finite open right cylinder of radius a with symmetry axis along the z-axis, base at z = 0, and of height h)