Author: Daniel Mentrard

r

r

V_{cylinder} = π r² h

V_{cone}=?

Transfer water

             Cylinder

              Cone

  \frac{ 3 }{ 3 } π \;  r³  +  \frac{ 1 }{ 3 } π \;  r³  =  \frac{ 4 }{ 3 } π \;  r³

V= \frac{ 1 }{3 } π r²h

B_1 = (-1.269434919291537, -0.24888440446039067)
View3D = (3.382715164898048, 1.2123744703469022)
xa: x(View3D)
sinphi: sin(xa)
cosphi: cos(xa)
ya: y(View3D)
sintheta: sin(ya)
Zoom = 0.8 (slider from 0.1 to 5, step 0.1)
xy: -(Zoom) * cosphi * sintheta
X: (x(B_1) + Zoom * sinphi, y(B_1) + xy)
a = 0 (slider from 0 to 1, step 0.1)
height = 1.5 (slider from 0.1 to 5, step 0.1)
O = (4.769824005151069, 1.3838715633236394)
radius = 1.1 (slider from 0.1 to 2, step 0.1)
costheta: cos(ya)
Y: (x(B_1) + Zoom * cosphi, y(B_1) + Zoom * sinphi * sintheta)
v = Vector(B_1, Y)
Z: (x(B_1) + 0.0, y(B_1) + Zoom * costheta)
w = Vector(B_1, X)
C = Translate(O, Vector[height * w])
u = Vector(B_1, Z)
A_3 = Translate(O, Vector[radius * u])
a_2 = OrthogonalLine(View3D, yAxis)
b_2 = OrthogonalLine(View3D, xAxis)
c: cos(ya)
d = Segment(O, A_3)
B = Translate(O, Vector[radius * v])
e = Segment(O, B)
D = Mirror(B, O)
E = Mirror(A_3, O)
h_1 = Segment(D, O)
i = Segment(E, O)
F = Midpoint(B, A_3)
G = Midpoint(B, F)
H = Midpoint(O, G)
I = Midpoint(H, G)
J = Mirror(I, G)
f = Conic(A_3, J, B, E, D)
j = Segment(C, A_3)
l = Segment(C, B)
m_2 = Segment(C, E)
n_2 = Segment(C, D)
p = Line(F, O)
K = Midpoint(B, E)
q = Line(K, O)
L, M = Intersect(f, p)
N, P = Intersect(f, q)
r = Segment(C, N)
s = Segment(C, L)
t = Segment(C, P)
a1 = Segment(C, M)
b1 = Segment(C, O)
H1 = (2.2276318033782596, 1.333431241859893)
z = Vector(O, H1)
p1 = Translate(f, z)
I1 = Translate(C, z)
u1 = Vector(H1, I1)
q1 = Translate(p1, u1)
J1 = Translate(D, z)
K1 = Translate(N, z)
M1 = Translate(A_3, z)
N1 = Translate(M, z)
O1 = Translate(L, z)
P1 = Translate(E, z)
Q1 = Translate(P, z)
R1 = Translate(B, z)
S1 = Translate(J1, u1)
T1 = Translate(K1, u1)
U1 = Translate(M1, u1)
V1 = Translate(N1, u1)
W1 = Translate(R1, u1)
Z1 = Translate(Q1, u1)
A'2 = Translate(O1, u1)
B2 = Translate(P1, u1)
l1 = Segment(S1, J1)
m1 = Segment(T1, K1)
n1 = Segment(U1, M1)
r1 = Segment(V1, N1)
s1 = Segment(W1, R1)
t1 = Segment(Z1, Q1)
a2 = Segment(B2, P1)
b2 = Segment(A'2, O1)
g2 = Segment(I1, H1)
h2 = Segment(H1, M1)
o = 0.036 (slider from -5 to 5, step 0.001)
L1 = Sequence(Translate[p1, i * u1], i, 0.0, 1.0, o)
L2 = Sequence(Dilate[f, i, C], i, 0.0, 1.0, o)
J_1 = Midpoint(h2)
L_1 = Midpoint(d)
M_1 = (0.827567950382497, 1.8369314084706818)
N_1 = (0.827567950382497, 1.5076070891575644)
O_1 = (0.6894255586591542, 1.6682954506742287)
P_1 = (0.9772936045488216, 1.6655559163178855)
QQ = (2.9418398197977416, 1.7143434161350717)
R_1 = (3.1834957725684174, 1.7165936441925638)
S_1 = (2.927900543568472, 1.5846634237549007)
T_1 = (3.1645667339253136, 1.576524623538127)
f'_2 = Dilate(f, a, C)
p1' = Translate(p1, Vector[a / 3.0 * u1])
p1'_1 = Translate(p1, Vector[1.0 / 3.0 * u1])
p1'_2 = Translate(p1, Vector[2.0 / 3.0 * u1])
U_1 = (2.158344047229324, 1.3665826871197109)
liste11 = Sequence(Dilate[f, i, C], i, a, 1.0, o)
m = 5 (slider from -5 to 5, step 0.1)
n = 20 (slider from -5 to 20, step 1)
liste1 = Sequence(Translate[p1, i * u1], i, 0.0, a / 3.0, o)
texte2: "radius=" + radius + "
height =" + height
texte5: "radius=" + radius + "
height =" + height