Spherical cap

In geometry, a spherical cap, spherical dome, or spherical segment of one base is a portion of a sphere cut off by a plane. If the plane passes through the center of the sphere, so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere.

If the radius of the base of the cap is ${\displaystyle a}$ , and the height of the cap is ${\displaystyle h}$, then the volume of the spherical cap is

and the curved surface area of the spherical cap is

or

The relationship between ${\displaystyle h}$ and ${\displaystyle r}$ is irrelevant as long as ${\displaystyle 0\leq h\leq 2r}$ . The red section of the illustration is also a spherical cap.

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