# Sphere

- Sphere (a three-dimensional figure) has all points equally spaces from a given point of a three dimensional solid.
- Lune of a sphere is the space occupied by a wedge from the center of the sphere to the surface of the sphere.
- Sector of a sphere is the space occupied by a portion of the sphere with the vertex at the center and conical boundary.
- Segment and zone of a sphere is the space occupied by a portion of the sphere cut by two parallel planes.
- Sperical cap is the space occupied by a portion of the sphere cut by a plane.
- See Moment of Inertia of a Sphere

### Circumference of a Sphere formula

\(\large{ C= 2 \; \pi \; r }\)

\(\large{ C= \pi \; d }\)

Where:

\(\large{ C }\) = circumference

\(\large{ d }\) = diameter

\(\large{ r }\) = radius

\(\large{ \pi }\) = Pi

### Diameter of a Sphere formula

\(\large{ d = 2\;r }\)

Where:

\(\large{ d }\) = diameter

\(\large{ r }\) = radius

### Luna of a Sphere Formula

(Eq. 1) \(\large{ S = 2\;r^2 \;theta }\)

(Eq. 2) \(\large{ S = \frac{\pi}{90} \;r^2 \;alpha }\)

(Eq. 1) \(\large{ V = \frac{2}{3} \;r^3 \;theta }\)

(Eq. 2) \(\large{ V = \frac{\pi}{270} \;r^3 \;alpha }\)

Where:

\(\large{ S }\) = surface area

\(\large{ V }\) = volume

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

### Sector of a sphere formula

(Eq. 1) \(\large{ S = 2\; \pi \;r \;h }\)

(Eq. 2) \(\large{ S = \pi \;r\; \left( 2\;h+r \right) }\)

(Eq. 1) \(\large{ V = \frac {2}{3}\; \pi \; r^2\;h }\)

(Eq. 2) \(\large{ V = \frac {2\; \pi \; r^2\;h}{3} }\)

Where:

\(\large{ S }\) = surface area

\(\large{ V }\) = volume

\(\large{ h }\) = height

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

\(\large{ r_1 }\) = radius

### Segment and Zone of a Sphere Formula

\(\large{ S = 2\; \pi \;r \;h }\)

\(\large{ V = \frac{\pi}{6} \; \left(3\;r_1^2+ 3\;r_2^2+h^2\right)\;h }\)

Where:

\(\large{ S }\) = surface area

\(\large{ V }\) = volume

\(\large{ h }\) = height

\(\large{ \pi }\) = Pi

\(\large{ r_1 }\) = radius

\(\large{ r_2 }\) = radius of the top

### Spherical Cap Formula

\(\large{ r = \frac{h^2\;+\;r_2^2}{2\;h} }\)

\(\large{ S = 2\; \pi \;r \;h }\)

Where:

\(\large{ S }\) = surface area

\(\large{ h }\) = height

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

### Surface Area of a sphere Formula

\(\large{ S = 2\; \pi \;r^2 }\)

Where:

\(\large{ S }\) = surface area

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

### Volume of a sphere Formula

\(\large{ V = \frac{4}{3} \; \pi \;r^3 }\)

Where:

\(\large{ V }\) = volume

\(\large{ \pi }\) = Pi

\(\large{ r }\) = radius

Tags: Equations for Volume