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

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

2

S = 2 a L cos^(-1)((a - h)/a)

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

dA = a du dv

x^_ = piecewise | {L/2, 0, (2 (h (2 a - h))^(3/2))/(3 (a - h) sqrt(h (2 a - h)) - 3 a^2 csc^(-1)(a/sqrt(h (2 a - h))))} | h<=a {L/2, 0, (2 (h (2 a - h))^(3/2))/(3 a^2 (cot^(-1)((a - h)/sqrt(h (2 a - h))) - 2 sec^(-1)(a/sqrt(h (2 a - h)))) + 3 (a - h) sqrt(h (2 a - h)))} | h>a

V = L (a^2 cos^(-1)((a - h)/a) - (a - h) sqrt(2 a h - h^2))

K(u, v) = 0

(for a segment of a finite right cylinder of radius a with symmetry axis along the x-axis, bases at x = 0 and x = L, and cut parallel to the xy-plane at a height h above the bottom of the cylinder)

E(u, v) = 1 F(u, v) = 0 G(u, v) = a^2

e(u, v) = 0 f(u, v) = 0 g(u, v) = a

left double bracketing bar x(u, v) right double bracketing bar = sqrt(a^2 + v^2)

N^^(u, v) = (0, -cos(u), -sin(u))

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