Volume (cm³) =

1-1-36

1-2-18

1-3-12

1-4-9

1-6-6

2-2-9

2-3-6

3-3-4

Solutions GM64

Aire minimale

Modifier

v = 36 (slider from -5 to 100, step 1)
a_c: cbrt(v)
v_c: a_c
A = Intersect(xAxis, yAxis)
B = (6, 2)
a = OrthogonalLine(B, xAxis)
b = OrthogonalLine(B, yAxis)
C = Intersect(a, xAxis)
D = Intersect(b, yAxis)
poly1, a_1, c, b_1, d = Polygon(A, C, B, D)
E = (6, 6)
e = Line(A, E)
f = Line(B, e)
g = Line(D, e)
h = Line(C, e)
ChampTexte1 = Textfield(v)
largeur: a_1
longueur: d
airebase: largeur * longueur
profondeur: v / airebase
r: profondeur / 2
k = Circle(A, r)
F = Intersect(k, e, 2)
i = Line(F, d)
G = Intersect(g, i)
j = Line(G, b)
H = Intersect(f, j)
l = Line(H, a)
m = Line(F, a_1)
I = Intersect(h, l)
poly2, c_1, b_2, h_1, i_1 = Polygon(C, B, H, I)
poly3, d_1, b_3, h_2, g_1 = Polygon(D, B, H, G)
poly4, a_2, f_1, g_2, d_2 = Polygon(A, F, G, D)
poly5, g_3, f_2, i_2, h_3 = Polygon(G, F, I, H)
poly6, a_3, c_2, i_3, f_3 = Polygon(A, C, I, F)
texte1: "Largeur = " + largeur + " cm"
texte2: "Hauteur = " + longueur + " cm"
texte3: "Profondeur = " + profondeur + " cm"
n = Segment(A, C)
p = Segment(C, I)
q = Segment(I, H)
s = Segment(H, B)
t = Segment(B, C)
e_1 = Segment(B, D)
j_1 = Segment(D, A)
k_1 = Segment(D, G)
l_1 = Segment(G, H)
m_1 = Segment(A, F)
n_1 = Segment(F, G)
p_1 = Segment(F, I)
J = Midpoint(p)
texte4: "Aire face bleue = " + largeur + " · " + longueur + " = " + poly1 + " cm²"
w: largeur * profondeur
w_1: longueur * profondeur
texte5_1: "Aire face rouge =  " + largeur + " · " + profondeur + " = " + w + "  cm²"
texte5: "Aire face verte = " + longueur + " · " + profondeur + " = " + w_1 + " cm²"
q_1 = Segment(G, B)
K = Midpoint(q_1)
texte6: "" + w + ""
r_1 = Segment(C, H)
L = Midpoint(r_1)
texte7: "" + w_1 + ""
s_1 = Segment(A, B)
M = Midpoint(s_1)
texte8: "" + poly1 + ""
w_3: (poly1 + w + w_1) * 2
texte9: "Aire totale = (" + poly1 + " + " + w + " + " + w_1 + ") · 2 = " + w_3 + " cm²"
texte4_2: "" + profondeur + ""
o = false
ChampText1 = 36
u = false
z = false
o_1 = true