Volume Of Sphere

The maine idea in this app is to use capacity as equivalent of volume. It uses 4 cone of radius the radius of the sphere and height the radius of the sphere also. The animation transfers the water of the cones to fill the sphere. So, the volume of the sphere equals 4 times the volume of one cone.

$\huge注水$

Reset

Anim

V=\frac{1}{3} π r^2h

V=\frac{4}{3} π r^3

h

h

h

h

r

r

r

r

r

$\scalebox{1.7}圆锥体积$

$\scalebox{1.7}球体体积$

h=r

t = 0 (slider from 0 to 1, step 0.001)
A: (0, -4, 2)
B: (0, -1, 2)
C: (0, 2, 2)
D: (0, 5, 2)
E: (0, -4, 3.5)
F: (0, -1, 3.5)
G: (0, 2, 3.5)
H: (0, 5, 3.5)
I: (0, 0, 0)
r: 1.5
a = Sphere(I, r + 0.5)
b, c, d = Cone(E, A, r)
e, f, g = Cone(F, B, r)
h, k, i = Cone(G, C, r)
j, p, l = Cone(H, D, r)
m: (-t)
n: z = (1.5 * (1 - t)) + 2
q = IntersectPath(n, d)
o, s, t_1 = Cone(Center[q], A, Radius[q])
c_1 = IntersectPath(n, g)
u, d_1, v = Cone(Center[c_1], B, Radius[c_1])
e_1 = IntersectPath(n, i)
w, f_1, a_1 = Cone(Center[e_1], C, Radius[e_1])
g_1 = IntersectPath(n, l)
b_1, h_1, i_1 = Cone(Center[g_1], D, Radius[g_1])
k_1 = IntersectPath(z = -2 + (4 * t), a)
l1 = Zip(Segment[Q, Q + (0, 1.5, 0)], Q, {E, F, G, H})
l2 = Zip(Segment[P, Q], P, {A, B, C, D}, Q, {E, F, G, H})
m_1 = false
n_1 = false
a1 = Sphere(I, r)
l_1 = Segment(I, I + (0, 1.5, 0))
J = PointIn(a1)
j_1 = Segment(A, J)
K = PointIn(a1)
p_1 = Segment(B, K)
L = PointIn(a1)
q_1 = Segment(C, L)
M = PointIn(a1)
r_1 = Segment(D, M)
o_1 = Surface((r; ϕ; θ), ϕ, 0, 360°, θ, -90°, (((2 * t) - 1) * 90°))