Question

A cube is painted blue on all faces and is cut into 125 cubes of equal size. How many cubes are not painted on any face

Answer 1

Cube problems are quite a lengthy one

But there are some formulas which can help you in solving these problems in seconds

So before solving this problem

Let's just learn some basic concepts about Cubes

1. IF a cube is painted then the corner cubes will have three sides painted ( 8 corner cubes)

2. Except for the corner , all the remaining cubes on the edges will have 2 sides painted

3. The number of cubes whose none of the sides are painted are the innermost portion when all the cubes from the surfaces are removed

So it is crystal clear that the number of cubes asked in the question are the innermost cubes ..

As per the question, a cube was painted blue and divided into 125 pieces i.e 4 cuts were given on each surface

125 = 4 4 4

i.e we will get 5×5×5 pieces on each surface by making 4cuts each

To find the cubes which are not painted on any face

Lets just apply a formula

No face painted cubes = ( n-2)^3

=(5–2)^3 ( n= the number of smaller cubes)

=(3)^3

=27✓

Answer 2

Answer: There are 27 cubes that are not painted at all.

Step-by-step explanation:

Since we have given that

Number of cubes of equal size = 125

So, number of cubes in a row would be

$\sqrt[3]{125}=5$

so, we need to find the number of cubes that are not painted on any face.

As we know that the number of cubes that are not painted on any face is given by

$(n-2)^3=(5-2)^3=3^3=27$

Hence, there are 27 cubes that are not painted at all.