A spherical sector is a portion of a sphere, defined by a central angle (\( \theta \)) and a radius. It is the 3D equivalent of a sector in a circle. The sector is shaped like a "pie slice," with a central angle that forms the "slice" of the sphere. It's a region bounded by two radii and the arc of a great circle.
\[ V = \frac{2}{3} \pi R^2 h \]
This formula calculates the volume of the spherical sector. It's derived by considering the sector's portion of the sphere and integrating the volume within the boundaries of the sector.
\[ A = \pi R (r + 2h) \]
Here, \( r \) is the radius of the base circle of the sector, and \( h \) is the height from the base to the top. This formula gives the total surface area, including the spherical curved surface and the base circle.