Sphere

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.

Sphere Index

 

sphere 3

Circumference of a Sphere formula

\(\large{ C = 2 \; \pi \; r }\)
Symbol English Metric
\(\large{ C }\) = circumference \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ d }\) = diameter \(\large{ in }\) \(\large{ mm }\)

 

sphere 3

Diameter of a Sphere formula

\(\large{ d = 2\;r }\)
Symbol English Metric
\(\large{ d }\) = diameter \(\large{ in }\) \(\large{ mm }\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

 

 

sphere 3

RADIUS of a sphere formula

\(\large{ r =  \sqrt{  \frac{ S }{ 4 \; \pi }  }  }\) 

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

Symbol English Metric
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ S }\) = surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)

 

sphere 3

Surface Area of a sphere formula

\(\large{ S =  4\; \pi \;r^2  }\) 
Symbol English Metric
\(\large{ S }\) = surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

 

 

sphere 3

Volume of a sphere formula

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

\(\large{ V =  \frac{ \pi \; d^3 }{ 6 }  }\) 

Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

sphere volume cap 1

Surface Area of a sphere Cap formula

\(\large{ S = 2 \; \pi \; r \; h  }\) 
Symbol English Metric
\(\large{ S }\) = surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

 

sphere volume cap 1

VOLUME of a sphere Cap formula

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

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

Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_1 }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

sphere diameter 1

Surface Area of a sphere Segment formula

\(\large{ S = 2 \; \pi \; r \; h  }\) 
Symbol English Metric
\(\large{ S }\) = surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

 

sphere diameter 1

VOLUME of a sphere Segment formula

\(\large{ V = \frac {1}{6} \; \pi\;h \left( 3 r_1{^2} + 3 r_2{^2} + h^2  \right)  }\) 
Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_1 }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_2 }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

sphere volume wedge 1

Surface Area of a sphere WEDGE formula

\(\large{ S = \frac{ \theta }{ 360 } \; 4 \; \pi \; r^2 }\) 
Symbol English Metric
\(\large{ S }\) = surface area \(\large{ in^2 }\) \(\large{ mm^2 }\)
\(\large{ \theta }\) = angle \(\large{ deg }\) \(\large{ rad }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

 

sphere volume wedge 1

Volume of a sphere WEDGE formula

\(\large{ V = \frac{ \theta }{ 2 \; \pi } \; \frac{ 4 }{ 3 } \; \pi \; r^2 }\) 
Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ \theta }\) = angle \(\large{ deg }\) \(\large{ rad }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

 

sphere volume sector 1

VOLUME of a sphere SECTOR formula

\(\large{ V = \frac {2}{3}\; \pi \; r^2\;h }\) 
Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)
\(\large{ h }\) = height \(\large{ in }\) \(\large{ mm }\)
\(\large{ \pi }\) = Pi  \(\large{3.141 592 653 ...}\)
\(\large{ r }\) = radius \(\large{ in }\) \(\large{ mm }\)
\(\large{ r_1 }\) = radius \(\large{ in }\) \(\large{ mm }\)

 

Piping Designer Logo 1

 

 

 

Tags: Volume Area Segment Sector