sphericalcap

A spherical cap is a portion of a sphere cut off by a plane. Imagine slicing the top off an orange with a knife; the peel that is removed forms a spherical cap. The boundary of the cap is a circle, and the cap itself has a curved surface and a flat circular base. The key features of a spherical cap are its height, the radius of its base, and the radius of the sphere from which it is cut.

The volume of a spherical cap can be calculated using a specific formula. This formula depends on the radius of the sphere and the height of the cap. Similarly, the surface area of the curved part of the cap can also be determined. These formulas are derived using calculus, involving integration of infinitesimal elements of the sphere.

Spherical caps have various applications in geometry and physics. For example, they can be used to model domes, the lenses in some optical instruments, or even the shape of certain celestial bodies. Understanding the properties and calculations associated with spherical caps is important in fields that deal with curved surfaces and three-dimensional shapes.