Question

A cube of side 4 cm is painted with blue colour.It is cut into smaller cubes of 1 cm.Then, how many smaller cubes have paint on at least one face

Answer 1

Answer:

40

Step-by-step explanation:

volume of 4cm. sided cube = 4³ = 64 cm³

then number of faces(1cm²) painted = 6x4² = 96

number of smaller cubes have paint on at least one face = those painted on ( 2 , 3) faces = 12x2 + 8x2 = 40 cubes

Answer 2

Logical Reasoning

Side of larger cube is 4cm.

Side of smaller cube is 1 cm.

Larger cube is painted with blue color.

The smaller cubes that are cut is separated.

Total number of cubes we will get after cutting larger cube is $\frac{4\times 4\times4}{1\times 1\times1}=64 \ small\ cubes$

The number of cubes having at least one face painted will include,

total number of cubes minus (no. of cubes having one face painted + no. of cubes having two face painted + no. of cubes having three face painted )

So, of cubes having only three face painted is cubes situated at corners of big cubes, which is 8.

Number of cubes having only two faces painted  is number of cubes at edges excluding corner cubes, hence 12 cubes.

Number of cubes having only one face painted is the cube at center of each face, hence 24 such cubes will be there.

Hence, cubes with no face painted is $(n-2)^3=(4-2)^3=8$

Hence , no. of cubes having at least one side painted is 56.