Question

19. There is a Cube whose dimensions are 4 x 4 x 4 cm.Now the cube is cut into small cubes of side 1 cm.
How many small cubes have three faces coloured ?​

Answer 1

Given :

The dimensions of a cube is 4 × 4 × 4 cm. and colored with all its outer sides.

Now the cube is cut into small cubes of side 1 cm.

To Find :

The number of cubes have three faces coloured.

Solution :

Let the number of cubes be 'n'

The volume of the larger cube = The volume of 'n' small cubes.

(side of bigger cube)³ = n (side of one small cube)³  

[since volume of a cube = side³]

4³ = n (1³)

n =  $\frac{4\times 4\times 4}{1\times 1\times 1}$

n = 64

Therefore, number of small cubes will be 64.

Since the large cube is painted on all 6 faces.

There are 8 small cubes which have three faces coloured.

This is clearly shown in the figure attached.