Comparaison de volumes
Author: Guy Gervais
Date: 19 novembre 2011

Exercice permettant de comparer le volume d'un cône et d'un cylindre selon la hauteur du liquide. Vous pouvez observer le cône ou le cylindre (cases à cocher) et déplacer la "Hauteur de l'eau". Essayez avec le bouton animer!

Hauteur de l'eau

Rayon

Volume cône

Volume d'eau

Hauteur de l'eau

Variation du volume d'eau dans un
cône en fonction de sa hauteur

Animer

Tracer la fonction

Volume cylindre

Cylindre

Cône

Tracer la fonction

Crée par Guy Gervais

h_l = 1.001 (slider from 0.0010 to 7, step 0.1)
B = (11, 1)
A = (7, 1)
a = Line(A, B)
C = Point(a)
k = Circle(C, h_l)
b = OrthogonalLine(C, a)
H = Intersect(k, b, 2.0)
j = OrthogonalLine(H, b)
h = 7 (slider from 0 to 10, step 0.1)
d = Circle(C, h)
E = Intersect(d, b, 2.0)
distanceEH = Distance(E, H)
r = 0.9 (slider from 0.2 to 1.5, step 0.1)
c = Circle(C, r)
D = Intersect(c, a, 2.0)
i = Segment(E, D)
J = Intersect(j, i)
distanceHJ = Distance(H, J)
e = Circle(D, 0.1)
F = Intersect(e, a, 1.0)
TexteHJ: Name[H] + (Name[J]) + " \, = \, " + distanceHJ
l: 3.141592653589793 * r^(2.0) * h / 3.0
m: 3.141592653589793 * distanceHJ^(2.0) * distanceEH / 3.0
n: l - m
TexteEH: Name[E] + (Name[H]) + " \, = \, " + distanceEH
V: (h_l, n)
p = Circle(J, 0.1)
K = Intersect(p, j, 2.0)
K' = Mirror(K, b)
q = Ellipse(K, K', J)
s = Segment(C, E)
t = Segment(C, D)
a_1 = Segment(H, J)
o = false
VT: V
u = false
L = (2.995054462131343, 16.463965755330637)
M = (2.995054462131343, 14.329929214097078)
N = (6.968734998392477, 14.329929214097078)
O = (6.968734998392477, 16.463965755330637)
poly2, l_1, m_1, n_1, o_1 = Polygon(L, M, N, O)
V_2: 3.141592653589793 * r^(2.0) * h_l
W: (h_l, V_2)
w = true
z = false
W_1: W
u_1 = false
m_2 = Segment(C, A)
D' = Mirror(D, C)
f = Semicircle(D, D')
g = Semicircle(D', D)
G = Intersect(j, i)
G' = Mirror(G, H)
b_1 = Segment(C, D')
c_1 = Segment(E, D')
d_1 = Semicircle(G, G')
e_1 = Semicircle(G', G)
f_1 = OrthogonalLine(D, t)
g_1 = OrthogonalLine(D', b_1)
h_1 = OrthogonalLine(E, f_1)
I = Intersect(f_1, h_1)
P = Intersect(g_1, h_1)
Q = Intersect(j, f_1)
R = Intersect(j, g_1)
k_1 = Semicircle(Q, R)
p_1 = Semicircle(R, Q)
q_1 = Semicircle(I, P)
r_1 = Semicircle(P, I)
poly1, d_2, g_2, g', d' = Polygon(D, G, G', D')
i_1 = Segment(D, G)
j_1 = Segment(G', D')
s_1 = Semicircle(D, D')
t_1 = Semicircle(D', D)
poly3, d_3, q_2, r_2, d'_1 = Polygon(D, Q, R, D')
a_2 = Segment(Q, D)
b_2 = Segment(R, D')
c_2 = Segment(I, D)
e_2 = Segment(P, D')
Z = (400, 400)