Sphere

Written by Jerry Ratzlaff on . Posted in Solid Geometry

  • sphere 2Sphere (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.

 

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sphere 3Circumference 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

 

sphere 3Diameter 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

 

sphere 3Surface 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

 

sphere volume cap 1Surface 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

 

sphere diameter 1Surface 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

 

sphere volume wedge 1Surface 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

 

sphere volume sector 1VOLUME 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

 

Tags: Equations for Volume Equations for Area Equations for Segment Equations for Sector