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