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Q.

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?

Chapter/Topic: Surface Areas and Volumes

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a

1

b

6

c

8

d

12

answer is B.

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Detailed Solution

Given, a cube is painted yellow on all six faces and then the cube cuts into 27 small cubes of equal parts. So it has been cut into an 3×3×3
arrangement. The image that comes to mind is a Rubik’s cube.
There is 1 cube in every centre (middle of 3 inch 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 2”

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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?Chapter/Topic: Surface Areas and Volumes