# Cube

Written by Jerry Ratzlaff on . Posted in Solid Geometry

• 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

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

### Where:

$$\large{ R }$$ = circumscribed sphere radius

$$\large{ a }$$ = edge

## Cube Circumscribed Sphere Volume 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 formulas

 $$\large{ a = \sqrt { \frac { A_s } { 6 } } }$$ $$\large{ a = V^{1/3} }$$ $$\large{ a = \sqrt { 3 } \; \frac { D' } {3} }$$

### Where:

$$\large{ a }$$ = edge

$$\large{ A_s }$$ = 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

 $$\large{ A_s = 6\;a^2 }$$

### Where:

$$\large{ A_s }$$ = 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: Volume Equations