Surface Area of a Spherical Cap

Problem

The surface area element of a sphere of radius R is R^2 * sin(phi) dphi dtheta, with phi the polar angle.

Integrating from the pole to phi_max gives the area of a spherical cap: 2 * pi * R^2 * (1 - cos(phi_max)). Given the radius and phi_max in radians, return the cap area.

Hint

A hemisphere is half the sphere area, matching the formula at phi_max = pi / 2.

Test cases

case 1

in: [1,1.5707963267948966]

expected: 6.283185307179585

case 2

in: [1,0]

expected: 0

case 3

in: [2,3.141592653589793]

expected: 50.26548245743669

case 4

in: [1,1.0471975511965976]

expected: 3.1415926535897922

Starter codePython

def spherical_cap_area(radius, phi_max):
    # Your code here
    pass

4 test cases · run your code against them in the editor