How much is half a glass?

At a restaurant recently, the waiter offered to fill my glass.

Since I was driving, I asked for just half a glass.

To what height should the glass be filled?

Full Glass

Half a Glass

a = 5.5 (slider from 0 to 10, step 0.1)
B = (20.05693359375, 86.91476590636256)
A = (19.974999999999998, 162.0168067226891)
b = Segment(A, B)
C = Point(b)
n = Segment(A, C)
K: C + (0, n / 10 a)
k = OrthogonalLine(K, b)
d = OrthogonalLine(C, b)
H = Point(d)
J = Mirror(H, C)
s = Segment(C, H)
c = OrthogonalLine(A, b)
G = Point(c)
g = Ray(G, H)
I = Mirror(G, A)
h = Ray(I, J)
N = Intersect(g, h)
b_1 = Segment(N, K)
a_1 = Segment(N, C)
q = Segment(A, G)
t = Segment(A, N)
e = OrthogonalLine(B, b)
D = Point(b)
E = Point(e)
F = Mirror(E, B)
Q, g_1, h_1, j, i = Polygon(G, H, J, I)
L = Intersect(k, g_1)
r = Segment(K, L)
M = Intersect(k, j)
R, l, m, j_1, h_2 = Polygon(L, M, J, H)
p = Segment(C, D)
T3: π r r b_1 / 3 - π a_1 s s / 3 + ""
Glass: π q q t / 3 - π a_1 s s / 3 + ""
X: (a, 0)
Y1: (0, (π q q t - π a_1 s s) / 3)
c_1 = OrthogonalLine(Y1, yAxis)
Y2: (0, (π q q t - π a_1 s s) / 6)
f_1 = OrthogonalLine(Y2, yAxis)
P: (a, π r r b_1 / 3 - π a_1 s s / 3)
S, f, d_1, e_1 = Polygon(D, E, F)
O = (1, 190)
T = (15, 190)
U = (15, 120)
V = (1, 120)
W, o, t_1, u, v = Polygon(O, T, U, V)
i_1 = Segment(P, X)
k_1 = OrthogonalLine(P, i_1)
Y = Intersect(k_1, yAxis)
l_1 = Segment(P, Y)