# 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.

## Circumference of a Sphere formulas

 $$\large{ C= 2 \; \pi \; r }$$ $$\large{ C= \pi \; d }$$

### 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

## RADIUS of a sphere formula

 $$\large{ r = \sqrt{ \frac{ S }{ 4 \; \pi } } }$$ $$\large{ r = \sqrt{ \frac{ 3 }{ 4 } \; \frac{ V }{ \pi } } }$$

### Where:

$$\large{ r }$$ = radius

$$\large{ \pi }$$ = Pi

$$\large{ S }$$ = surface area

$$\large{ V }$$ = volume

## Surface Area of a sphere formula

 $$\large{ S = 4\; \pi \;r^2 }$$

### Where:

$$\large{ S }$$ = surface area

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

## Volume of a sphere formula

 $$\large{ V = \frac{4}{3} \; \pi \;r^3 }$$ $$\large{ V = \frac{ \pi \; d^3 }{ 6 } }$$

### Where:

$$\large{ V }$$ = volume

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

## Surface Area of a sphere Cap formula

 $$\large{ S = 2 \; \pi \; r \; h }$$

### Where:

$$\large{ S }$$ = surface area

$$\large{ h }$$ = height

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

## VOLUME of a sphere Cap formula

 $$\large{ V = \frac {1}{3} \; \pi\;h^2 \left( 3 r - h \right) }$$ $$\large{ V = \frac {1}{6} \; \pi\;h \left( 3 r_1{^2} + h^2 \right) }$$

### Where:

$$\large{ V }$$ = volume

$$\large{ h }$$ = height

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

$$\large{ r_1 }$$ = radius

## Surface Area of a sphere Segment formula

 $$\large{ S = 2 \; \pi \; r \; h }$$

### Where:

$$\large{ S }$$ = surface area

$$\large{ h }$$ = height

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

## VOLUME of a sphere Segment formula

 $$\large{ V = \frac {1}{6} \; \pi\;h \left( 3 r_1{^2} + 3 r_2{^2} + h^2 \right) }$$

### Where:

$$\large{ V }$$ = volume

$$\large{ h }$$ = height

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

$$\large{ r_1 }$$ = radius

$$\large{ r_2 }$$ = radius

## Surface Area of a sphere WEDGE formula

 $$\large{ S = \frac{ \theta }{ 360 } \; 4 \; \pi \; r^2 }$$

### Where:

$$\large{ S }$$ = surface area

$$\large{ \theta }$$ = angle

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

## Volume of a sphere WEDGE formula

 $$\large{ V = \frac{ \theta }{ 2 \; \pi } \; \frac{ 4 }{ 3 } \; \pi \; r^2 }$$

### Where:

$$\large{ V }$$ = volume

$$\large{ \theta }$$ = angle

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

## VOLUME of a sphere SECTOR formula

 $$\large{ V = \frac {2}{3}\; \pi \; r^2\;h }$$

### Where:

$$\large{ V }$$ = volume

$$\large{ h }$$ = height

$$\large{ \pi }$$ = Pi

$$\large{ r }$$ = radius

$$\large{ r_1 }$$ = radius