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 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

Luna of a Sphere formulas

 $$\large{ S = 2\;r^2 \;theta }$$ $$\large{ S = \frac{\pi}{90} \;r^2 \;alpha }$$ $$\large{ V = \frac{2}{3} \;r^3 \;theta }$$ $$\large{ V = \frac{\pi}{270} \;r^3 \;alpha }$$

Where:

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

$$\large{ V }$$ = volume

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

$$\large{ r }$$ = radius

Sector of a sphere formulas

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

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 formulas

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

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 formulas

 $$\large{ r = \frac{h^2\;+\;r_2^2}{2\;h} }$$ $$\large{ S = 2\; \pi \;r \;h }$$

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