# Formulas For Cube And Cuboid

## Cube and Cuboid Formulas :

## Cuboid :

A Cuboid is a closed 3-dimensional geometrical figure bounded by six rectangular plane regions.

A Cuboid is made up of six rectangles, each of the rectangle is called the face. In the figure above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are the 6-faces of cuboid. The top face ABCD and bottom face EFGH form a pair of opposite faces. Similarly, ABFE, DCGH, and DAEH, CBFG are pairs of opposite faces.

## 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*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*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 sidess painted= 8(always)
- For a cuboid of dimension a*b*c painted on all sides which is cut into smaller cubes of dimension 1*1*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 sidess painted= 8

## Directions to Solve Cube and Cuboid Formulas

### Question 1.

**How many cubes have only one coloured face each ?**

(A) 32

(B) 8

(C) 16

(D) 0

#### Answer: Option C

#### Explanation:

8 from (I) and 8 from (II)

Therefore 8 from each.

### Question 2.

**What is the number of cubes with at least one green face each ?**

(A) 36

(B) 32

(C) 48

(D) 38

#### Answer: Option C

#### Explanation:

24 from (I) and 14 from (II)

### Question 3.

**How many cubes have each one red and another green ?**

(A) 0

(B) 8

(C) 16

(D) 24