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)	Calculate the Volume of a Circular Cylinder.
`vol_cone`(→ float)	Calculate the Volume of a Cone.
`vol_conical_frustum`(→ float)	Calculate the Volume of a Conical Frustum.
`vol_cube`(→ float)	Calculate the Volume of a Cube.
`vol_cuboid`(→ float)	Calculate the Volume of a Cuboid.
`vol_hemisphere`(→ float)	Calculate the volume of a hemisphere
`vol_hollow_circular_cylinder`(→ float)	Calculate the Volume of a Hollow Circular Cylinder.
`vol_icosahedron`(→ float)	Calculate the Volume of an Icosahedron.
`vol_prism`(→ float)	Calculate the Volume of a Prism.
`vol_pyramid`(→ float)	Calculate the Volume of a Pyramid.
`vol_right_circ_cone`(→ float)	Calculate the Volume of a Right Circular Cone.
`vol_sphere`(→ float)	Calculate the Volume of a Sphere.
`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)	Calculate the Volume of a Torus.

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 :return pi * radius^2 * 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 :return (1/3) * area_of_base * 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. :return 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 :return 2/3 * pi * 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) :return V = Bh >>> 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) :return (1/3) * Bh >>> 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 :return (1/3) * pi * radius^2 * 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 :return (4/3) * pi * 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 (h1, h2) of the spherical caps, then the two volumes and it returns the sum. The height formulas are h1 = (radius_1 - radius_2 + centers_distance)

h2 = (radius_2 - radius_1 + centers_distance)

(radius_2 + radius_1 - centers_distance)

/ (2 * centers_distance)

if centers_distance is 0 then it returns the volume of the smallers sphere :return vol_spherical_cap(h1, radius_2) + vol_spherical_cap(h2, 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 (v1, v2) of the spheres, then the volume of the intersection (i) and it returns the sum v1+v2-i. If centers_distance is 0 then it returns the volume of the larger sphere :return vol_sphere(radius_1) + vol_sphere(radius_2)

>>> 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 :return 2pi^2 * torus_radius * 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

maths.volume¶

Functions¶

Module Contents¶

thealgorithms-python

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