def cylinder_surface_area(radius, height) -> Unit("m²"):
"""
Compute the surface area (side + top + bottom)
"""
radius = normalize_numeric(radius)
height = normalize_numeric(height)
return cylinder_side_surface_area(radius, height) + 2 * circle_area(radius)
def cylinder_side_surface_area(radius, height) -> Unit("m²"):
"""
Compute the surface area of the side (also called ")
"""
radius = normalize_numeric(radius)
height = normalize_numeric(height)
return 2 * math.pi * radius * height
def cylinder_volume(radius, height) -> Unit("m³"):
"""
Compute the volume of a cylinder by its radius and height
"""
radius = normalize_numeric(radius)
height = normalize_numeric(height)
return math.pi * (radius**2) * height
def hollow_cylinder_inner_radius_by_volume(outer_radius, volume, height) -> Unit("m"):
"""
Given the outer radius, the height and the inner radius of a hollow cylinder,
compute the inner radius
"""
outer_radius = normalize_numeric(outer_radius)
volume = normalize_numeric(volume)
height = normalize_numeric(height)
# Wolfram Alpha: solve V=(pi*o²*h)-(pi*i²*h) for i
term1 = np.pi*height*(outer_radius**2)-volume
# Due to rounding errors etc, term1 might become negative.
# This will lead to sqrt(-x) => NaN but we actually treat it as a zero result
if term1 < 0.:
return 0
# Default case
return np.sqrt(term1)/(np.sqrt(np.pi) * np.sqrt(height))
def circle_circumference(radius) -> Unit("m"):
"""
Compute the circumference of a circle from its radius
"""
radius = normalize_numeric(radius)
return 2. * math.pi * radius
def circle_area(radius) -> Unit("m²"):
"""
Compute the enclosed area of a circle from its radius
"""
radius = normalize_numeric(radius)
return math.pi * radius**2
def hollow_cylinder_volume(outer_radius, inner_radius, height) -> Unit("m³"):
"""
Compute the volume of a hollow cylinder by its height and the inner and outer radii
"""
return cylinder_volume(outer_radius, height) - cylinder_volume(inner_radius, height)