Use sliders to change the radius and height of the cone.
“l” is the slant height of the cone.
r/l is the ratio of the radius to the slant height.  
It is also equal to the radian measure of the central angle of the sector in circle F.

radius = 1.9 (slider from 0 to 10, step 0.1)
height = 4.3 (slider from 0 to 10, step 0.1)
A = (-2.88, -2.9)
B_1 = (0.82, -2.94)
a = Line(A, B_1)
b = OrthogonalLine(A, a)
c = Circle(A, height)
C = Intersect(c, b, 2)
d = Circle(A, radius)
B = Intersect(d, a, 2)
l = Segment(C, B)
r = Segment(A, B)
h = Segment(C, A)
E = (2.62, 0.34)
e = Circle(E, r)
F = (11.94, 0.28)
f = Circle(F, l)
ratio: ((r / l * 2) * π)
G = Point(f)
H = Rotate(G, ratio, F)
α = Angle(G, F, H)
k = CircleSector(F, G, H)
D = Point(e)
D' = Rotate(D, 6.283167853887067, E)
β = Angle(D, E, D')
p = CircleSector(E, D, D')