Cube

on . Posted in Solid Geometry

  • cube 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 7

Cube Circumscribed Sphere Radius formula

\(\large{ R =  a \;  \frac{ \sqrt {3} }{2}   }\) 
Symbol English Metric
\(\large{ R }\) = circumscribed sphere radius \(\large{ in }\)  \(\large{ mm }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

 

 

cube 7

Circumscribed Sphere Volume of a Cube formula

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

 

 

cube 12

Edge of a Cube formulas

\(\large{ a =   \sqrt { \frac { A_s } { 6 } } }\) 

\(\large{ a = V^{1/3} }\) 

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

Symbol English Metric
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)
\(\large{ D' }\) = space diagonal \(\large{ in }\) \(\large{ mm }\)
\(\large{ A_s }\) = surface face area \(\large{ in }\) \(\large{ mm }\)
\(\large{ V }\) = volume \(\large{ in^3 }\) \(\large{ mm^3 }\)

 

 

cube 12

Face Area of a Cube formula

\(\large{ A_{area} = a^2 }\) 
Symbol English Metric
\(\large{ A_{area} }\) = face area \(\large{ in^2 }\)  \(\large{ mm^2 }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

 

 

cube 8

 Inscribed Radius of a Cube formula

\(\large{ r = \frac{a}{2}   }\) 
Symbol English Metric
\(\large{ r }\) = inside radius \(\large{ in }\)  \(\large{ mm }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

 

 

cube 8

Inscribed Sphere Volume of a Cube formula

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

 

 

cube 9

Midsphere Radius of a Cube formula

\(\large{ r_m =  \frac{a}{2} \sqrt {2}   }\) 
Symbol English Metric
\(\large{ r_m }\) = midsphere radius \(\large{ in }\)  \(\large{ mm }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)


 

 

 

cube 6

Space Diagonal of a Cube formula

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

 

 

 

cube 12

Surface face Area of a Cube formula

\(\large{ A_s = 6\;a^2 }\) 
Symbol English Metric
\(\large{ A_s }\) = surface face area \(\large{ in^2 }\)  \(\large{ mm^2 }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

 

 

cube 12

Surface to volume ratio of a Cube formula

\(\large{ S_v = \frac{6}{a} }\) 
Symbol English Metric
\(\large{ S_v }\) = surface to volume ratio \(\large{ in^3 }\)  \(\large{ mm^3 }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

 

 

cube 12

Volume of a Cube formula

\(\large{ V =   a^3 }\) 
Symbol English Metric
\(\large{ V }\) = volume \(\large{ in^3 }\)  \(\large{ mm^3 }\) 
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

 

 

 

cube 12

Weight of a Cube formula

\(\large{ m =   a^3  \rho }\) 
Symbol English Metric
\(\large{ m }\) = mass \(\large{ lbm }\)  \(\large{ kg }\) 
\(\large{ \rho }\)   (Greek symbol rho) = density \(\large{\frac{lbm}{ft^3}}\) \(\large{\frac{kg}{m^3}}\)
\(\large{ a }\) = edge \(\large{ in }\) \(\large{ mm }\)

 

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Tags: Volume