The formula for the area of a spherical cap

A spherical cap refers to a portion of a sphere that has been cut off, leaving a flat cross-section. The area formula for the spherical cap introduced in this article does not include the area of the cross-section.

The surface area formula for a spherical segment is S = 2πRh, where R is the radius of the sphere and h is the height of the spherical segment.

For example, consider a pool shaped like a spherical segment with a sphere radius of 5 meters and a segment height of 4 meters. To find the surface area of the pool, we use the formula S = 2πRh. Substituting the given values, we get S = 2π × 5 × 4 = 40π ≈ 125.66 square meters.

The challenges of the spherical segment area formula lie in understanding the concept of a spherical segment and determining the parameters in the formula. A spherical segment refers to a part of a sphere that has been cut off, leaving a flat cross-section. When calculating the area of a spherical segment, it is necessary to determine the sphere’s radius R, the radius of the base of the spherical segment r, and the height of the segment h. These parameters must be determined based on specific circumstances.