Question

A big cube is painted with black, blue and red colour on pair of opposite faces. ‘N’ cuts are made on each axis of this cube and 64 small cubes are obtained. Which of the following statement(s) is/are NOT correct?

I. Value of ‘N’ is 4.

II. Number of cubes having one face black, one face red and all other faces unpainted are 8.

1. Both I and II
2. Only II
3. Only I
4. Neither I nor II

Answer 1

Correct Answer - Option 3 : Only I

As per the question, "N" numbers of cuts are made and 64 small cubes are obtained.

I. Value of ‘N’ is 4:

Formula Used: For the number of cuts:

 \(2^{N} =\) Number of small cubes

N = Number of Cuts.

\(2^{N} = 64\)

\(2^{N} = 2^{6}\)

N = 6.

Therefore, statement 1 is wrong.

statement 2: 

Whenever an n*n*n cube is given and is painted on all sides and we need to find the number of smaller cubes that are not painted we can simply calculate (n - 2)(n - 2)(n - 2)

So in this case we are given a 4 × 4 × 4 cube.

Hence the number of cubes that will have no face coloured is:

(4 - 2)(4 - 2)(4 - 2)

= 2 × 2 × 2

= 8

Therefore, conclusion 2 is correct.

Thus it is concluded that statement(s) 1 is/are NOT correct.

Hence, the correct answer is "Only I".