Cube
Cube (a three-dimensional figure) is a regular polyhedron with square faces.- All edges are the same length.
- All faces are squares
- Diagonal is a line from one vertices to another that is non adjacent.
- Circumscribed sphere is a polyhedron is a sphere that contains the polyhedron and touches each of the ployhedron's vertices.
- Inscribed sphere - A convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.
- Midsphere is a polyhedron is a sphere that is tangent to every edge of the polyhedron.
- 4 base diagonals
- 24 face diagonals
- 4 space diagonals
- 12 edges
- 6 faces
- 8 vertex
Cube Circumscribed Sphere Radius formula |
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| \(\large{ R = a \; \frac{ \sqrt {3} }{2} }\) | ||
| Symbol | English | Metric |
| \(\large{ R }\) = circumscribed sphere radius | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Circumscribed Sphere Volume of a Cube formula |
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| \(\large{ C_v = \frac{3}{4} \; \pi \; \left( a\; \frac{ \sqrt {3} }{2} \right) ^3 }\) | ||
| Symbol | English | Metric |
| \(\large{ C_v }\) = circumscribed sphere volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
Edge of a Cube formulas |
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\(\large{ a = \sqrt { \frac { A_s } { 6 } } }\) \(\large{ a = V^{1/3} }\) \(\large{ a = \sqrt { 3 } \; \frac { D' } {3} }\) |
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| Symbol | English | Metric |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ D' }\) = space diagonal | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ A_s }\) = surface face area | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ V }\) = volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
Face Area of a Cube formula |
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| \(\large{ A_{area} = a^2 }\) | ||
| Symbol | English | Metric |
| \(\large{ A_{area} }\) = face area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Inscribed Radius of a Cube formula |
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| \(\large{ r = \frac{a}{2} }\) | ||
| Symbol | English | Metric |
| \(\large{ r }\) = inside radius | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Inscribed Sphere Volume of a Cube formula |
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| \(\large{ I_v = \frac{3}{4} \; \pi \; \left( \frac{ a }{2} \right) ^3 }\) | ||
| Symbol | English | Metric |
| \(\large{ I_v }\) = inscribed sphere volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ \pi }\) = Pi | \(\large{3.141 592 653 ...}\) | |
Midsphere Radius of a Cube formula |
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| \(\large{ r_m = \frac{a}{2} \sqrt {2} }\) | ||
| Symbol | English | Metric |
| \(\large{ r_m }\) = midsphere radius | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Space Diagonal of a Cube formula |
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| \(\large{ D' = \sqrt {3} \;a }\) | ||
| Symbol | English | Metric |
| \(\large{ D' }\) = space diagonal | \(\large{ in }\) | \(\large{ mm }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Surface face Area of a Cube formula |
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| \(\large{ A_s = 6\;a^2 }\) | ||
| Symbol | English | Metric |
| \(\large{ A_s }\) = surface face area | \(\large{ in^2 }\) | \(\large{ mm^2 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Surface to volume ratio of a Cube formula |
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| \(\large{ S_v = \frac{6}{a} }\) | ||
| Symbol | English | Metric |
| \(\large{ S_v }\) = surface to volume ratio | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Volume of a Cube formula |
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| \(\large{ V = a^3 }\) | ||
| Symbol | English | Metric |
| \(\large{ V }\) = volume | \(\large{ in^3 }\) | \(\large{ mm^3 }\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Weight of a Cube formula |
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| \(\large{ m = a^3 \rho }\) | ||
| Symbol | English | Metric |
| \(\large{ m }\) = mass | \(\large{ lbm }\) | \(\large{ kg }\) |
| \(\large{ \rho }\) (Greek symbol rho) = density | \(\large{\frac{lbm}{ft^3}}\) | \(\large{\frac{kg}{m^3}}\) |
| \(\large{ a }\) = edge | \(\large{ in }\) | \(\large{ mm }\) |
Tags: Volume