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 $\frac{1}{6} \pi h(3a^2+h^2)$ and the surface area of the spherical cap is $2 \pi r h \,\!$ . [1]