Question

A cube of side $4cm$ is painted black on all of its surfaces and then divided into various smaller cubes of side $1cm$ each. The smaller cubes so obtained are separated.
Total no. of cubes obtained $=\frac{4\times 4\times 4}{1\times 1\times 1}=64$

Here $n=\frac{\text{side of big cube}}{\text{side of small cube}}=\frac{4}{1}=4$
How many smaller cubes have two surfaces painted?

• A. $8$
• B. $4$
• C. $24$
• D. $16$

Answer 1

Answer: (C)

The cubes with $2$ faces painted will be the cubes on the sides except the corner ones.
Therefore, face on the top and bottom will have $8+8=16$ cubes and the front and the back face will have $4+4=8$ cubes.
The cubes on the other two faces have been covered by the above four.
Therefore, total number of cubes $=8+16=24$.