Spherical cap

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In geometry, a spherical cap 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 sphere is called $r$ , the radius of the base of the cap called $a$ , and the height of the cap called $h$ , the volume of the spherical cap is then $\scriptstyle \pi h (3a^2 + h^2)/6$ and the curved surface area of the spherical cap is $\scriptstyle 2 \pi r h$ . [1]

Note also that in the upper hemisphere of the diagram, $\scriptstyle h = r - \sqrt{r^2 - a^2}$ , and in the lower hemisphere $\scriptstyle h = r + \sqrt{r^2 - a^2}$ .