Question

A cube, painted yellow on all faces is cut into 27 small cubes of equal size. How many small cubes are painted on only one face?
A.1
B.6
C.8
D.12

Answer 1

Hint: The given problem is easy if you have some imagination of cubes. For example, Rubik’s cube has alignment \[3 \times 3 \times 3\]. In Rubik’s cube if you count the number of cubes you will find 27 cubes of equal size. That is exactly the case in our problem. We need to find the number cubes painted on one side only.

Complete step-by-step answer:
Given, a cube is painted yellow on all six faces and then the cube cuts into 27 small cubes of equal part. So it has been cut into an \[3 \times 3 \times 3\] arrangement. The image that comes to mind is a Rubik’s cube.
There is 1 cube in every centre (middle of 3in each axis direction i.e., longitudinal lateral and vertical) which has no colour.
On each of the 6 sides of the cube, there is a central smaller cube that is painted on one face.
There are 8 corners of the cube, which are painted on 3 surfaces.
Remaining 12 cubes are painted on 2 sides only.
Thus, only 6 sides of the cube are painted on one face.
So, the correct answer is “Option B”.

Note: In cube all sides are equal. 12 cubes are painted on 2 sides because on each side of the cube, there are 4 cubes at the middle of the edges. These are shared with one other side of the cube. A cube has 6 faces, 8 vertices and 12 edges. Imagine a cube and follow the explanation which is done above.