Cube

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

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

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

Edge of a Cube formulas
$a \;=\; \sqrt{ \dfrac{ A_s }{ 6 } }$ $a \;=\; V^{1/3}$ $a \;=\; \sqrt{ 3 } \cdot \dfrac{ D' }{ 3 }$
Symbol	English	Metric
$a$ = edge	$in$	$mm$
$D'$ = space diagonal	$in$	$mm$
$A_s$ = surface face area	$in$	$mm$
$V$ = volume	$in^3$	$mm^3$

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.
$r \;=\; \dfrac{ a }{ 2 }$
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.
$I_v \;=\; \dfrac{ 3 }{ 4 } \cdot \pi \cdot \left(\dfrac{ a }{ 2 } \right)^3$
Symbol	English	Metric
$I_v$ = inscribed sphere volume	$in^3$	$mm^3$
$a$ = edge	$in$	$mm$
$\pi$ = Pi	$3.141 592 653 ...$	$3.141 592 653 ...$

Midsphere Radius of a Cube formula Midsphere is a polyhedron is a sphere that is tangent to every edge of the polyhedron.
$r_m \;=\; \dfrac{ a }{ 2 } \cdot \sqrt {2}$
Symbol	English	Metric
$r_m$ = midsphere radius	$in$	$mm$
$a$ = edge	$in$	$mm$

Space Diagonal of a Cube formula
$D' \;=\; \sqrt {3} \cdot a$
Symbol	English	Metric
$D'$ = space diagonal	$in$	$mm$
$a$ = edge	$in$	$mm$

Surface face Area of a Cube formula
$A_s \;=\; 6 \cdot a^2$
Symbol	English	Metric
$A_s$ = surface face area	$in^2$	$mm^2$
$a$ = edge	$in$	$mm$

Surface to volume ratio of a Cube formula
$S_v \;=\; \dfrac{ 6 }{ a }$
Symbol	English	Metric
$S_v$ = surface to volume ratio	$in^3$	$mm^3$
$a$ = edge	$in$	$mm$