Question

after the surface area of cube is painted the cube is cut into 64 small cubes of same dimension how many scube does not have face painted one face painted to face painted three face painting​

Answer 1

No face = 8  , 1 Face = 24 , 2 Face = 24 , 3 Face = 24

Step-by-step explanation:

after the surface area of cube is painted the cube is cut into 64 small cubes of same dimension

64 = 4³

hence Cube is cut into 4 *4 * 4

Cubes with no face painted = (4 - 2)(4-2)(4 - 2)

= 2 * 2 * 2 = 8   cubes

Cubes with 1 face painted = 6  * ( 4 -2)(4 - 2)  = 24  cubes

Cubes with 2 face painted = 12 * ( 4 - 2)  = 24 cubes

Cubes with 3 face painted =  8

Shortcut Formulas :

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 sides painted= 8(always)

Learn more:

A cube having a side of 6 cm is painted red on all the faces and then ...

https://brainly.in/question/13052344

A cube is painted blue on all faces. It is cut into 125 smaller cubes of ...

https://brainly.in/question/13090631

Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

after the surface area of cube is painted the cube is cut into 64 small cubes of same dimension

64 = 4³

hence Cube is cut into 4 *4 * 4

Cubes with no face painted = (4 - 2)(4-2)(4 - 2)

= 2 * 2 * 2 = 8 cubes

Cubes with 1 face painted = 6 * ( 4 -2)(4 - 2) = 24 cubes

Cubes with 2 face painted = 12 * ( 4 - 2) = 24 cubes

Cubes with 3 face painted = 8

Shortcut Formulas :

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 sides painted= 8(always)