Cube And Cuboid Shapes Formulas

Cube:

A cuboid having its length, breadth, height all to be equal in measurement is called as a cube.

A cube is a solid bounded by six square plane regions, where the side of the cube is called edge.

Formulas for Cube :

• For a cube of side n x n x n painted on all sides which is uniformly cut into smaller cubes of dimension 1 x 1 x 1,
• Number of cubes with 0 side painted= (n-2) ^{3}
• Number of cubes with 1 sides painted = 6(n – 2) ^{2}
• Number of cubes with 2 sides painted = 12(n-2)
• Number of cubes with 3 sides painted= 8(always)

Cuboid : 

All the edges of Cuboid are Not Equal. i.e Measures of Length , breadth and height are not equal.

A Cuboid is made up of six rectangles, each of the rectangle is called the face.

Formulas for Cuboid :

• For a cuboid of dimension a x b x c painted on all sides which is cut into smaller cubes of dimension 1 x 1 x 1,
• Number of cubes with 0 side painted = (a-2) (b-2) (c-2)
• Number of cubes with 1 sides painted = 2[(a-2) (b-2) + (b-2)(c-2) + (a-2)(c-2) ]
• Number of cubes with 2 sides painted = 4(a+b+c -6)
• Number of cubes with 3 sides painted = 8