Cube

Written by Jerry Ratzlaff on . Posted in Solid Geometry

  • cube 2cube 10Cube (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 7Circumscribed 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

cube 6Edge 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

cube 8Inscribed 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

cube 9Midsphere Radius of a Cube formula

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

Where:

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

\(\large{ a }\) = edge

 

 

 

 

cube 6Space 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