# Sphere

Written by Jerry Ratzlaff on . Posted in Solid Geometry

• 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