Question

A cube of 7 cm sides is painted black on all the sides and then cut into 1 cm sided small identical cubes. How many cubes have three faces painted?

• A. 4
• B. 8
• C. 49
• D. 72

Hint:

When cutting a cube into smaller cubes, the cubes at the corners will have three painted faces, while those along the edges will have two, and those on the faces will have one.

Answer 1

The Correct Option is B

We are given a cube of side 7 cm, which is painted black on all sides. The cube is then cut into 1 cm sided smaller cubes. This means the original cube is cut into \( 7^3 = 343 \) smaller cubes.
Identify the cubes with three painted faces The cubes with three painted faces are the ones located at the 8 corners of the large cube. These cubes are at the intersection of three faces.
Since there are 8 corners in a cube, there will be exactly 8 smaller cubes with three faces painted.
Thus, the number of cubes with three faces painted is \( \boxed{8} \).