Question

A cube is coloured red on all its faces .It is then cut into 64 smaller cubes of equal size

Answer 1

plz mark my answer as brainlist
you have written half question
question :A cube is painted red on all faces and it is cut into 64 small cubes of equal size. How many cubes are not painted?


answer

8
solutions :

In total it will become 4×4×4= 64. i.e; L×B×H

Cubes painted on three side =8

2 side = 2×12 = 24

1 side = 4×6 = 24

Then 24+24+8 will become 56.

It means that the cubes painted with no side will be 64 - 56= 8.

Ans. 8

Answer 2

Given: A cube is coloured red on all its faces .It is then cut into 64 smaller cubes of equal size.

To find: How many smaller cubes have no face coloured.

Solution: 8 smaller cubes have no face coloured.

The total number of smaller cubes is 64 according to the question. If the large cube is cut into 64 cubes then that means that the large cube must be a 4x4x4 cube.

$\sqrt[3]{64}= 4$

$face = 4*4$

       $= 16$

Thus, each face of the large cube has 16 smaller cubes. Now, in order to calculate the number of cubes that have no colour on them, the following formula can be calculated.

$(n-2)(n-2)(n-2)$

Here, n is the side of the cube which is 4 units.

$(4-2)(4-2)(4-2) = 2*2*2$

                                 $= 8$

Therefore, 8 smaller cubes have no face coloured.

Although part of your question is missing, you might be referring to this full question:  

A cube is coloured red on all of its faces. It is then cut into 64 smaller cubes of equal size. How many smaller cubes have no face coloured?