@@ -20,6 +20,56 @@ def vol_cube(side_length: int | float) -> float:
2020 return pow (side_length , 3 )
2121
2222
23+ def vol_spherical_cap (height : float , radius : float ) -> float :
24+ """
25+ Calculate the Volume of the spherical cap.
26+ :return 1/3 pi * height ^ 2 * (3 * radius - height)
27+
28+ >>> vol_spherical_cap(1, 2)
29+ 5.235987755982988
30+ """
31+ return 1 / 3 * pi * pow (height , 2 ) * (3 * radius - height )
32+
33+
34+ def vol_spheres_intersect (
35+ radius_1 : float , radius_2 : float , centers_distance : float
36+ ) -> float :
37+ """
38+ Calculate the volume of the intersection of two spheres.
39+
40+ The intersection is composed by two spherical caps and therefore its volume is the
41+ sum of the volumes of the spherical caps. First it calculates the heights (h1, h2)
42+ of the the spherical caps, then the two volumes and it returns the sum.
43+ The height formulas are
44+ h1 = (radius_1 - radius_2 + centers_distance)
45+ * (radius_1 + radius_2 - centers_distance)
46+ / (2 * centers_distance)
47+ h2 = (radius_2 - radius_1 + centers_distance)
48+ * (radius_2 + radius_1 - centers_distance)
49+ / (2 * centers_distance)
50+ if centers_distance is 0 then it returns the volume of the smallers sphere
51+ :return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, radius_1)
52+
53+ >>> vol_spheres_intersect(2, 2, 1)
54+ 21.205750411731103
55+ """
56+ if centers_distance == 0 :
57+ return vol_sphere (min (radius_1 , radius_2 ))
58+
59+ h1 = (
60+ (radius_1 - radius_2 + centers_distance )
61+ * (radius_1 + radius_2 - centers_distance )
62+ / (2 * centers_distance )
63+ )
64+ h2 = (
65+ (radius_2 - radius_1 + centers_distance )
66+ * (radius_2 + radius_1 - centers_distance )
67+ / (2 * centers_distance )
68+ )
69+
70+ return vol_spherical_cap (h1 , radius_2 ) + vol_spherical_cap (h2 , radius_1 )
71+
72+
2373def vol_cuboid (width : float , height : float , length : float ) -> float :
2474 """
2575 Calculate the Volume of a Cuboid.
@@ -127,6 +177,8 @@ def main():
127177 print ("Pyramid: " + str (vol_pyramid (2 , 2 ))) # ~= 1.33
128178 print ("Sphere: " + str (vol_sphere (2 ))) # ~= 33.5
129179 print ("Circular Cylinder: " + str (vol_circular_cylinder (2 , 2 ))) # ~= 25.1
180+ print ("Spherical cap: " + str (vol_spherical_cap (1 , 2 ))) # ~= 5.24
181+ print ("Spheres intersetion: " + str (vol_spheres_intersect (2 , 2 , 1 ))) # ~= 21.21
130182
131183
132184if __name__ == "__main__" :
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