Question

a cube of 4 cm has been painted on its surface in such a way that two opposite surfaces
have been painted blue and two adjacent surfaces have been painted red. two remaining surface have been left unpainted. now the cube is cut into smaller cube of 1 cm each.

how many cube have no side painted

how many cubes will have at least red colour on its surface

Answer 1

Step-by-step explanation:

volume of painted box= (4×4)2+2×4×2=48cm^3

volume of unpainted box=64-52=12cm^3

number of unpainted cubes 12.

number of cubes of red 2×4×2+4×3=28-14=14 red cubes

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Answer 2

Given: A cube of 4 cm has been painted on its surface in such a way that two opposite surfaces have been painted blue and two adjacent surfaces have been painted red. two remaining surface have been left unpainted. now the cube is cut into smaller cube of 1 cm each.

To find:

(1) How many cube have no side painted.  

(2) How many cubes will have at least red colour on its surface.

Solution:

(1) 192 cubes have no side painted.  

(2) 32 cubes will have at least red colour on its surface.

According to the question, the length of the side of the cube is 4 cm and it is cut into cubes of side 1 cm each. This means that each face would have 16 cubes (4*4). The number of smaller cubes would be 256.

1.

Now, four faces out of the six are painted. Thus, the total number of cubes that have paint on them is

$4*16 = 64$

So, the number of cubes that have no paint on them is

$256 - 64 = 192$

2.

According to the question, two adjacent faces of the cube have been painted red. So, the faces with at least red colour on them is

$2* 16 = 32$

Therefore,

(1) 192 cubes have no side painted.  

(2) 32 cubes will have at least red colour on its surface.