maths.volume

Find the volume of various shapes.

• https://en.wikipedia.org/wiki/Volume

• https://en.wikipedia.org/wiki/Spherical_cap

Functions

main()	Print the Results of Various Volume Calculations.
vol_circular_cylinder(→ float)
vol_cone(→ float)
vol_conical_frustum(→ float)
vol_cube(→ float)	Calculate the Volume of a Cube.
vol_cuboid(→ float)	Calculate the Volume of a Cuboid.
vol_hemisphere(→ float)
vol_hollow_circular_cylinder(→ float)	Calculate the Volume of a Hollow Circular Cylinder.
vol_icosahedron(→ float)
vol_prism(→ float)
vol_pyramid(→ float)
vol_right_circ_cone(→ float)
vol_sphere(→ float)
vol_spheres_intersect(→ float)	Calculate the volume of the intersection of two spheres.
vol_spheres_union(→ float)	Calculate the volume of the union of two spheres that possibly intersect.
vol_spherical_cap(→ float)	Calculate the volume of the spherical cap.
vol_torus(→ float)

Module Contents

maths.volume.main()

Print the Results of Various Volume Calculations.

maths.volume.vol_circular_cylinder(radius: float, height: float) → float

Calculate the Volume of a Circular Cylinder.

Wikipedia reference: https://en.wikipedia.org/wiki/Cylinder

Returns:

\(\pi \cdot radius^2 \cdot height\)

>>> vol_circular_cylinder(1, 1)
3.141592653589793
>>> vol_circular_cylinder(4, 3)
150.79644737231007
>>> vol_circular_cylinder(1.6, 1.6)
12.867963509103795
>>> vol_circular_cylinder(0, 0)
0.0
>>> vol_circular_cylinder(-1, 1)
Traceback (most recent call last):
    ...
ValueError: vol_circular_cylinder() only accepts non-negative values
>>> vol_circular_cylinder(1, -1)
Traceback (most recent call last):
    ...
ValueError: vol_circular_cylinder() only accepts non-negative values

maths.volume.vol_cone(area_of_base: float, height: float) → float

Calculate the Volume of a Cone.

Wikipedia reference: https://en.wikipedia.org/wiki/Cone

Returns:

\(\frac{1}{3} \cdot area\_of\_base \cdot height\)

>>> vol_cone(10, 3)
10.0
>>> vol_cone(1, 1)
0.3333333333333333
>>> vol_cone(1.6, 1.6)
0.8533333333333335
>>> vol_cone(0, 0)
0.0
>>> vol_cone(-1, 1)
Traceback (most recent call last):
    ...
ValueError: vol_cone() only accepts non-negative values
>>> vol_cone(1, -1)
Traceback (most recent call last):
    ...
ValueError: vol_cone() only accepts non-negative values

maths.volume.vol_conical_frustum(height: float, radius_1: float, radius_2: float) → float

Calculate the Volume of a Conical Frustum.

Wikipedia reference: https://en.wikipedia.org/wiki/Frustum

>>> vol_conical_frustum(45, 7, 28)
48490.482608158454
>>> vol_conical_frustum(1, 1, 2)
7.330382858376184
>>> vol_conical_frustum(1.6, 2.6, 3.6)
48.7240076620753
>>> vol_conical_frustum(0, 0, 0)
0.0
>>> vol_conical_frustum(-2, 2, 1)
Traceback (most recent call last):
    ...
ValueError: vol_conical_frustum() only accepts non-negative values
>>> vol_conical_frustum(2, -2, 1)
Traceback (most recent call last):
    ...
ValueError: vol_conical_frustum() only accepts non-negative values
>>> vol_conical_frustum(2, 2, -1)
Traceback (most recent call last):
    ...
ValueError: vol_conical_frustum() only accepts non-negative values

maths.volume.vol_cube(side_length: float) → float

Calculate the Volume of a Cube.

>>> vol_cube(1)
1.0
>>> vol_cube(3)
27.0
>>> vol_cube(0)
0.0
>>> vol_cube(1.6)
4.096000000000001
>>> vol_cube(-1)
Traceback (most recent call last):
    ...
ValueError: vol_cube() only accepts non-negative values

maths.volume.vol_cuboid(width: float, height: float, length: float) → float

Calculate the Volume of a Cuboid.

Returns:

multiple of width, length and height

>>> vol_cuboid(1, 1, 1)
1.0
>>> vol_cuboid(1, 2, 3)
6.0
>>> vol_cuboid(1.6, 2.6, 3.6)
14.976
>>> vol_cuboid(0, 0, 0)
0.0
>>> vol_cuboid(-1, 2, 3)
Traceback (most recent call last):
    ...
ValueError: vol_cuboid() only accepts non-negative values
>>> vol_cuboid(1, -2, 3)
Traceback (most recent call last):
    ...
ValueError: vol_cuboid() only accepts non-negative values
>>> vol_cuboid(1, 2, -3)
Traceback (most recent call last):
    ...
ValueError: vol_cuboid() only accepts non-negative values

maths.volume.vol_hemisphere(radius: float) → float

Calculate the volume of a hemisphere

Wikipedia reference: https://en.wikipedia.org/wiki/Hemisphere

Other references: https://www.cuemath.com/geometry/hemisphere

Returns:

\(\frac{2}{3} \cdot \pi \cdot radius^3\)

>>> vol_hemisphere(1)
2.0943951023931953
>>> vol_hemisphere(7)
718.377520120866
>>> vol_hemisphere(1.6)
8.57864233940253
>>> vol_hemisphere(0)
0.0
>>> vol_hemisphere(-1)
Traceback (most recent call last):
    ...
ValueError: vol_hemisphere() only accepts non-negative values

maths.volume.vol_hollow_circular_cylinder(inner_radius: float, outer_radius: float, height: float) → float

Calculate the Volume of a Hollow Circular Cylinder.

>>> vol_hollow_circular_cylinder(1, 2, 3)
28.274333882308138
>>> vol_hollow_circular_cylinder(1.6, 2.6, 3.6)
47.50088092227767
>>> vol_hollow_circular_cylinder(-1, 2, 3)
Traceback (most recent call last):
    ...
ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
>>> vol_hollow_circular_cylinder(1, -2, 3)
Traceback (most recent call last):
    ...
ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
>>> vol_hollow_circular_cylinder(1, 2, -3)
Traceback (most recent call last):
    ...
ValueError: vol_hollow_circular_cylinder() only accepts non-negative values
>>> vol_hollow_circular_cylinder(2, 1, 3)
Traceback (most recent call last):
    ...
ValueError: outer_radius must be greater than inner_radius
>>> vol_hollow_circular_cylinder(0, 0, 0)
Traceback (most recent call last):
    ...
ValueError: outer_radius must be greater than inner_radius

maths.volume.vol_icosahedron(tri_side: float) → float

Calculate the Volume of an Icosahedron.

Wikipedia reference: https://en.wikipedia.org/wiki/Regular_icosahedron

>>> from math import isclose
>>> isclose(vol_icosahedron(2.5), 34.088984228514256)
True
>>> isclose(vol_icosahedron(10), 2181.694990624912374)
True
>>> isclose(vol_icosahedron(5), 272.711873828114047)
True
>>> isclose(vol_icosahedron(3.49), 92.740688412033628)
True
>>> vol_icosahedron(0)
0.0
>>> vol_icosahedron(-1)
Traceback (most recent call last):
    ...
ValueError: vol_icosahedron() only accepts non-negative values
>>> vol_icosahedron(-0.2)
Traceback (most recent call last):
    ...
ValueError: vol_icosahedron() only accepts non-negative values

maths.volume.vol_prism(area_of_base: float, height: float) → float

Calculate the Volume of a Prism.

Wikipedia reference: https://en.wikipedia.org/wiki/Prism_(geometry)

Returns:

\(V = B \cdot h\)

>>> vol_prism(10, 2)
20.0
>>> vol_prism(11, 1)
11.0
>>> vol_prism(1.6, 1.6)
2.5600000000000005
>>> vol_prism(0, 0)
0.0
>>> vol_prism(-1, 1)
Traceback (most recent call last):
    ...
ValueError: vol_prism() only accepts non-negative values
>>> vol_prism(1, -1)
Traceback (most recent call last):
    ...
ValueError: vol_prism() only accepts non-negative values

maths.volume.vol_pyramid(area_of_base: float, height: float) → float

Calculate the Volume of a Pyramid.

Wikipedia reference: https://en.wikipedia.org/wiki/Pyramid_(geometry)

Returns:

\(\frac{1}{3} \cdot B \cdot h\)

>>> vol_pyramid(10, 3)
10.0
>>> vol_pyramid(1.5, 3)
1.5
>>> vol_pyramid(1.6, 1.6)
0.8533333333333335
>>> vol_pyramid(0, 0)
0.0
>>> vol_pyramid(-1, 1)
Traceback (most recent call last):
    ...
ValueError: vol_pyramid() only accepts non-negative values
>>> vol_pyramid(1, -1)
Traceback (most recent call last):
    ...
ValueError: vol_pyramid() only accepts non-negative values

maths.volume.vol_right_circ_cone(radius: float, height: float) → float

Calculate the Volume of a Right Circular Cone.

Wikipedia reference: https://en.wikipedia.org/wiki/Cone

Returns:

\(\frac{1}{3} \cdot \pi \cdot radius^2 \cdot height\)

>>> vol_right_circ_cone(2, 3)
12.566370614359172
>>> vol_right_circ_cone(0, 0)
0.0
>>> vol_right_circ_cone(1.6, 1.6)
4.289321169701265
>>> vol_right_circ_cone(-1, 1)
Traceback (most recent call last):
    ...
ValueError: vol_right_circ_cone() only accepts non-negative values
>>> vol_right_circ_cone(1, -1)
Traceback (most recent call last):
    ...
ValueError: vol_right_circ_cone() only accepts non-negative values

maths.volume.vol_sphere(radius: float) → float

Calculate the Volume of a Sphere.

Wikipedia reference: https://en.wikipedia.org/wiki/Sphere

Returns:

\(\frac{4}{3} \cdot \pi \cdot r^3\)

>>> vol_sphere(5)
523.5987755982989
>>> vol_sphere(1)
4.1887902047863905
>>> vol_sphere(1.6)
17.15728467880506
>>> vol_sphere(0)
0.0
>>> vol_sphere(-1)
Traceback (most recent call last):
    ...
ValueError: vol_sphere() only accepts non-negative values

maths.volume.vol_spheres_intersect(radius_1: float, radius_2: float, centers_distance: float) → float

Calculate the volume of the intersection of two spheres.

The intersection is composed by two spherical caps and therefore its volume is the sum of the volumes of the spherical caps. First, it calculates the heights \((h_1, h_2)\) of the spherical caps, then the two volumes and it returns the sum. The height formulas are

\[ \begin{align}\begin{aligned}h_1 = \frac{(radius_1 - radius_2 + centers\_distance) \cdot (radius_1 + radius_2 - centers\_distance)} {2 \cdot centers\_distance}\\h_2 = \frac{(radius_2 - radius_1 + centers\_distance) \cdot (radius_2 + radius_1 - centers\_distance)} {2 \cdot centers\_distance}\end{aligned}\end{align} \]

if centers_distance is 0 then it returns the volume of the smallers sphere

Returns:

vol_spherical_cap (\(h_1\), \(radius_2\)) + vol_spherical_cap (\(h_2\), \(radius_1\))

>>> vol_spheres_intersect(2, 2, 1)
21.205750411731103
>>> vol_spheres_intersect(2.6, 2.6, 1.6)
40.71504079052372
>>> vol_spheres_intersect(0, 0, 0)
0.0
>>> vol_spheres_intersect(-2, 2, 1)
Traceback (most recent call last):
    ...
ValueError: vol_spheres_intersect() only accepts non-negative values
>>> vol_spheres_intersect(2, -2, 1)
Traceback (most recent call last):
    ...
ValueError: vol_spheres_intersect() only accepts non-negative values
>>> vol_spheres_intersect(2, 2, -1)
Traceback (most recent call last):
    ...
ValueError: vol_spheres_intersect() only accepts non-negative values

maths.volume.vol_spheres_union(radius_1: float, radius_2: float, centers_distance: float) → float

Calculate the volume of the union of two spheres that possibly intersect.

It is the sum of sphere \(A\) and sphere \(B\) minus their intersection. First, it calculates the volumes \((v_1, v_2)\) of the spheres, then the volume of the intersection \(i\) and it returns the sum \(v_1 + v_2 - i\). If centers_distance is 0 then it returns the volume of the larger sphere

Returns:

vol_sphere (\(radius_1\)) + vol_sphere (\(radius_2\)) - vol_spheres_intersect (\(radius_1\), \(radius_2\), \(centers\_distance\))

>>> vol_spheres_union(2, 2, 1)
45.814892864851146
>>> vol_spheres_union(1.56, 2.2, 1.4)
48.77802773671288
>>> vol_spheres_union(0, 2, 1)
Traceback (most recent call last):
    ...
ValueError: vol_spheres_union() only accepts non-negative values, non-zero radius
>>> vol_spheres_union('1.56', '2.2', '1.4')
Traceback (most recent call last):
    ...
TypeError: '<=' not supported between instances of 'str' and 'int'
>>> vol_spheres_union(1, None, 1)
Traceback (most recent call last):
    ...
TypeError: '<=' not supported between instances of 'NoneType' and 'int'

maths.volume.vol_spherical_cap(height: float, radius: float) → float

Calculate the volume of the spherical cap.

>>> vol_spherical_cap(1, 2)
5.235987755982988
>>> vol_spherical_cap(1.6, 2.6)
16.621119532592402
>>> vol_spherical_cap(0, 0)
0.0
>>> vol_spherical_cap(-1, 2)
Traceback (most recent call last):
    ...
ValueError: vol_spherical_cap() only accepts non-negative values
>>> vol_spherical_cap(1, -2)
Traceback (most recent call last):
    ...
ValueError: vol_spherical_cap() only accepts non-negative values

maths.volume.vol_torus(torus_radius: float, tube_radius: float) → float

Calculate the Volume of a Torus.

Wikipedia reference: https://en.wikipedia.org/wiki/Torus

Returns:

\(2 \pi^2 \cdot torus\_radius \cdot tube\_radius^2\)

>>> vol_torus(1, 1)
19.739208802178716
>>> vol_torus(4, 3)
710.6115168784338
>>> vol_torus(3, 4)
947.4820225045784
>>> vol_torus(1.6, 1.6)
80.85179925372404
>>> vol_torus(0, 0)
0.0
>>> vol_torus(-1, 1)
Traceback (most recent call last):
    ...
ValueError: vol_torus() only accepts non-negative values
>>> vol_torus(1, -1)
Traceback (most recent call last):
    ...
ValueError: vol_torus() only accepts non-negative values