# 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

### Circumscribed Sphere Radius of a Cube formula

\(\large{ R = a \; \frac{ \sqrt {3} }{2} }\)

Where:

\(\large{ R }\) = circumscribed sphere radius

\(\large{ a }\) = edge

### Circumscribed Sphere Volume of a Cube formula

\(\large{ C_v = \frac{3}{4} \; \pi \; \left( a\; \frac{ \sqrt {3} }{2} \right) ^3 }\)

Where:

\(\large{ C_v }\) = circumscribed sphere volume

\(\large{ a }\) = edge

\(\large{ \pi }\) = Pi

### Edge of a Cube formula

\(\large{ a = \sqrt { \frac { A_{surface} } { 6 } } }\)

\(\large{ a = V^{1/3} }\)

\(\large{ a = \sqrt { 3 } \; \frac { D' } {3} }\)

Where:

\(\large{ a }\) = edge

\(\large{ A_{surface} }\) = surface face area

\(\large{ V }\) = volume

\(\large{ D' }\) = space diagonal

### Face Area of a Cube formula

\(\large{ A_{area} = a^2 }\)

Where:

\(\large{ A_{area} }\) = face area

\(\large{ a }\) = edge

### Inscribed Radius of a Cube formula

\(\large{ r = \frac{a}{2} }\)

Where:

\(\large{ r }\) = inside radius

\(\large{ a }\) = edge

### Inscribed Sphere Volume of a Cube formula

\(\large{ I_v = \frac{3}{4} \; \pi \; \left( \frac{ a }{2} \right) ^3 }\)

Where:

\(\large{ I_v }\) = circumscribed sphere volume

\(\large{ a }\) = edge

\(\large{ \pi }\) = Pi

### Midsphere Radius of a Cube formula

\(\large{ r_m = \frac{a}{2} \sqrt {2} }\)

Where:

\(\large{ r_m }\) = midsphere radius

\(\large{ a }\) = edge

### Space Diagonal of a Cube formula

\(\large{ D' = \sqrt {3} \;a }\)

Where:

\(\large{ D' }\) = space diagonal

\(\large{ a }\) = edge

### Surface face Area of a Cube formula

\(\large{ A_{surface} = 6\;a^2 }\)

Where:

\(\large{ A_{surface} }\) = surface face area

\(\large{ a }\) = edge

### Surface to volume ratio of a Cube formula

\(\large{ S_v = \frac{6}{a} }\)

Where:

\(\large{ S_v }\) = surface to volume ratio

\(\large{ a }\) = edge

### Volume of a Cube formula

\(\large{ V = a^3 }\)

Where:

\(\large{ V }\) = volume

\(\large{ a }\) = edge

Tags: Equations for Volume