# Cube

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 is 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

Circumscribed sphere is a polyhedron is a sphere that contains the polyhedron and touches each of the ployhedron's vertices.

$$R = a \; \sqrt {3} \;/\;2$$
Symbol English Metric
$$R$$ = circumscribed sphere radius $$in$$ $$mm$$
$$a$$ = edge $$in$$ $$mm$$

### Circumscribed Sphere Volume of a Cube formula

Circumscribed sphere is a polyhedron is a sphere that contains the polyhedron and touches each of the ployhedron's vertices.

$$C_v = (3\;/\;4) \; \pi \; ( a\; \sqrt{3} \;/\;2 )^3$$
Symbol English Metric
$$C_v$$ = circumscribed sphere volume $$in^3$$ $$mm^3$$
$$a$$ = edge $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$

### Edge of a Cube formulas

$$a = \sqrt{ A_s \;/\; 6 }$$

$$a = V^{1/3}$$

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

Symbol English Metric
$$a$$ = edge $$in$$ $$mm$$
$$D'$$ = space diagonal $$in$$ $$mm$$
$$A_s$$ = surface face area $$in$$ $$mm$$
$$V$$ = volume $$in^3$$ $$mm^3$$

### Face Area of a Cube formula

$$A_{area} = a^2$$
Symbol English Metric
$$A_{area}$$ = face area $$in^2$$ $$mm^2$$
$$a$$ = edge $$in$$ $$mm$$

### Inscribed Radius of a Cube formula

Inscribed sphere is a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

$$r = a\;/\;2$$
Symbol English Metric
$$r$$ = inside radius $$in$$ $$mm$$
$$a$$ = edge $$in$$ $$mm$$

### Inscribed Sphere Volume of a Cube formula

Inscribed sphere is a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

$$I_v = (3\;/\;4) \; \pi \; ( a \;/\;2 )^3$$
Symbol English Metric
$$I_v$$ = inscribed sphere volume $$in^3$$ $$mm^3$$
$$a$$ = edge $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$

### Midsphere Radius of a Cube formula

Midsphere is a polyhedron is a sphere that is tangent to every edge of the polyhedron.

$$r_m = (a\;/\;2)\; \sqrt {2}$$
Symbol English Metric
$$r_m$$ = midsphere radius $$in$$ $$mm$$
$$a$$ = edge $$in$$ $$mm$$

### Space Diagonal of a Cube formula

$$D' = \sqrt {3} \;a$$
Symbol English Metric
$$D'$$ = space diagonal $$in$$ $$mm$$
$$a$$ = edge $$in$$ $$mm$$

### Surface face Area of a Cube formula

$$A_s = 6\;a^2$$
Symbol English Metric
$$A_s$$ = surface face area $$in^2$$ $$mm^2$$
$$a$$ = edge $$in$$ $$mm$$

### Surface to volume ratio of a Cube formula

$$S_v = 6\;/\;a$$
Symbol English Metric
$$S_v$$ = surface to volume ratio $$in^3$$ $$mm^3$$
$$a$$ = edge $$in$$ $$mm$$

### Volume of a Cube formula

$$V = a^3$$
Symbol English Metric
$$V$$ = volume $$in^3$$ $$mm^3$$
$$a$$ = edge $$in$$ $$mm$$

### Weight of a Cube formula

$$m = a^3 \; \rho$$
Symbol English Metric
$$m$$ = mass $$lbm$$  $$kg$$
$$\rho$$   (Greek symbol rho) = density $$lbm\;/\;ft^3$$ $$kg\;/\;m^3$$
$$a$$ = edge $$in$$ $$mm$$

Tags: Volume Solid Prism