The surface of the sphere is the surface generated by a circumference that turns around its diameter. A sphere is the region of the space inside.
The elements of a sphere are:
 The center is the interior point equidistant to any point of the sphere.
 The radius is the distance of the center to a point of the sphere.
 The chord is the segment that joins any two points of the surface.
 The diameter is the chord that passes through the center.
 The poles are the points of the axis that are on the sphere's surface.
In addition to these elements, we can also define:
 The parallels are the circumferences obtained on cutting the sphere's surface with planes perpendicular to the axis of rotation.
 The equator is the circumference obtained on cutting the sphee's surface with the plane perpendicular to the axis of rotation that contains the center of the sphere.
 The meridians are the circumferences obtained on cutting the sphere's surface with planes that contain the rotation axis.
Geometric figures in the sphere

Hemisphere: It is each of the parts into which the sphere's surface is divided by a plane that passes through the center of the sphere, called diametral plane.

Semisphere: It is the volume of the hemisphere.

Spherical crescent: The spherical crescent is the part of the surface of a sphere in between two planes that cut at the diameter of the the sphere.
The area of the spherical crescent is $$A=\dfrac{4\cdot \pi \cdot r^2}{360}\cdot n$$, where $$n$$ is the angle between the two planes.

Spherical wedge: The spherical wedge is the part of a sphere in between two planes that cut though the diameter.
The volume of a spherical wedge is $$V=\dfrac{4}{3}\cdot\dfrac{\pi\cdot r^3}{360}\cdot n$$, where $$n$$ is the angle between the two planes.

Spherical skullcap: A spherical skullcap is each of the parts of the sphere determined by a cutting plane.
The area of the skullcap is $$A=2\cdot\pi\cdot R\cdot h$$.
The volume of the skullcap is $$V=\dfrac{1}{3}\cdot \pi\cdot h^2\cdot (3Rh)$$.

Spherical area: A spherical area is the part of the sphere in between two parallel cutting planes.
The area of the spherical area is $$A=2\cdot\pi\cdot R\cdot h$$.
The volume of the spherical area is $$V=\dfrac{1}{6}\cdot \pi\cdot h\cdot (h^2+3R^2+3 r^2)$$.