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 Artical Link - Moment of Inertia of a Sphere
Circumference of a Sphere formula |
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\(\large{ C = 2 \; \pi \; r }\) (Circumference of a Sphere) \(\large{ r = \frac{ C }{ 2 \; \pi } }\) |
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Solve for C
Solve for r
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| 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 | \(\large{ in }\) | \(\large{ mm }\) |
Diameter of a Sphere formula |
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\(\large{ d = 2\;r }\) (Diameter of a Sphere) \(\large{ r = \frac{d}{2} }\) |
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Solve for d
Solve for r
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| Symbol | English | Metric |
| \(\large{ d }\) = diameter | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
RADIUS of a sphere formula |
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\(\large{ r = \sqrt{ \frac{ S }{ 4 \; \pi } } }\) \(\large{ r = \sqrt{ \frac{ 3 }{ 4 } \; \frac{ V }{ \pi } } }\) |
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| 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 | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
Surface Area of a sphere formula |
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| \(\large{ S = 4\; \pi \;r^2 }\) | ||
| Symbol | English | Metric |
| \(\large{ S }\) = surface area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Volume of a sphere formula |
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\(\large{ V = \frac{4}{3} \; \pi \;r^3 }\) \(\large{ V = \frac{ \pi \; d^3 }{ 6 } }\) |
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| Symbol | English | Metric |
| \(\large{ V }\) = volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
| \(\large{ r }\) = radius | \(\large{ in }\) | \(\large{ mm }\) |
Surface Area of a sphere Cap formula |
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| \(\large{ S = 2 \; \pi \; r \; h }\) | ||
| 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 | \(\large{ in }\) | \(\large{ mm }\) |
VOLUME of a sphere Cap formula |
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\(\large{ V = \frac {1}{3} \; \pi\;h^2 \left( 3 r - h \right) }\) \(\large{ V = \frac {1}{6} \; \pi\;h \left( 3 r_1{^2} + h^2 \right) }\) |
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| 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 | \(\large{ in }\) | \(\large{ mm }\) |
Surface Area of a sphere Segment formula |
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| \(\large{ S = 2 \; \pi \; r \; h }\) | ||
| 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 | \(\large{ in }\) | \(\large{ mm }\) |
VOLUME of a sphere Segment formula |
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| \(\large{ V = \frac {1}{6} \; \pi\;h \left( 3 r_1{^2} + 3 r_2{^2} + h^2 \right) }\) | ||
| 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 | \(\large{ in }\) | \(\large{ mm }\) |
Surface Area of a sphere WEDGE formula |
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| \(\large{ S = \frac{ \theta }{ 360 } \; 4 \; \pi \; r^2 }\) | ||
| 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 | \(\large{ in }\) | \(\large{ mm }\) |
Volume of a sphere WEDGE formula |
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| \(\large{ V = \frac{ \theta }{ 2 \; \pi } \; \frac{ 4 }{ 3 } \; \pi \; r^2 }\) | ||
| 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 | \(\large{ in }\) | \(\large{ mm }\) |
VOLUME of a sphere SECTOR formula |
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| \(\large{ V = \frac {2}{3}\; \pi \; r^2\;h }\) | ||
| 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 | \(\large{ in }\) | \(\large{ mm }\) |
