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