S = 2 π a (a + h) (for a circular right cylinder with center at the origin, height h, radius a)

x^2 + y^2<=a^2 and -h/2<=z<=h/2

0

h

S_L = 2 π a h

x^_ = (0, 0, 0)

V = π a^2 h

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

max(2 a, sqrt(4 a^2 + h^2))

χ = 1