volume Algorithm

The volume Algorithm is a critical concept in the world of mathematics, specifically in the fields of geometry and calculus. It is a mathematical procedure used to determine the amount of space occupied by a 3-dimensional object, such as a cube, sphere, or cylinder. The volume algorithm varies depending on the shape of the object and is essential in solving various real-world problems related to designing structures, manufacturing, packaging, and fluid dynamics. The concept of volume finds its applications in many scientific and engineering disciplines, including physics, chemistry, and engineering. To compute the volume of a particular shape, one must use the appropriate formula that corresponds to the dimensions and characteristics of the object. For example, the volume of a cube is calculated using the formula V = a^3, where 'a' represents the length of any side, while the volume of a cylinder is determined by V = πr²h, with 'r' representing the radius of the base and 'h' being the height of the cylinder. These algorithms are derived from the principles of calculus and the use of integration techniques to find the exact volume of irregularly shaped objects. Moreover, volume algorithms play a vital role in modern technology, such as computer-aided design (CAD) software, 3D printing, and other fields where the accurate estimation of spatial parameters is necessary for optimal performance and efficiency.
"""
Find Volumes of Various Shapes.

Wikipedia reference: https://en.wikipedia.org/wiki/Volume
"""
from typing import Union
from math import pi, pow


def vol_cube(side_length: Union[int, float]) -> float:
    """
    Calculate the Volume of a Cube.

    >>> vol_cube(1)
    1.0
    >>> vol_cube(3)
    27.0
    """
    return pow(side_length, 3)


def 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
    """
    return float(width * height * length)


def 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
    """
    return area_of_base * height / 3.0


def 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
    """
    return pi * pow(radius, 2) * height / 3.0


def 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
    """
    return float(area_of_base * height)


def 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
    """
    return area_of_base * height / 3.0


def 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
    """
    return 4 / 3 * pi * pow(radius, 3)


def 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
    """
    return pi * pow(radius, 2) * height


def main():
    """Print the Results of Various Volume Calculations."""
    print("Volumes:")
    print("Cube: " + str(vol_cube(2)))  # = 8
    print("Cuboid: " + str(vol_cuboid(2, 2, 2)))  # = 8
    print("Cone: " + str(vol_cone(2, 2)))  # ~= 1.33
    print("Right Circular Cone: " + str(vol_right_circ_cone(2, 2)))  # ~= 8.38
    print("Prism: " + str(vol_prism(2, 2)))  # = 4
    print("Pyramid: " + str(vol_pyramid(2, 2)))  # ~= 1.33
    print("Sphere: " + str(vol_sphere(2)))  # ~= 33.5
    print("Circular Cylinder: " + str(vol_circular_cylinder(2, 2)))  # ~= 25.1


if __name__ == "__main__":
    main()

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