MathematicsA 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

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


  1. A
    1
  2. B
    6
  3. C
    8
  4. D
    12 

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    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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