Question

A cube is given with an edge of 12 units.it is painted on all faces and then cut into smaller cubes of edge of 4 units. how many cubes will have 2 faces painted?
a. 2
b. 12
c. 8
d. 0

Answer 1

Since this is a solid cube the number of cubes cut from it will be:

12/4=3
3×3×3=27

For us to solve this question, we need to literally draw the diagram and visualize it.

When we draw this diagram, we find that.

At the top and bottom corners, the painted faces are 3.

At the top and bottom centers along the height, the faces painted are two, and this gives 8 cubes.

At the top and bottom centers across the width and the length are 4 cubes.

This gives a total of 12 cubes.

Answer 2

Solution :-

A cube has 6 faces and none of the smaller cubes have all faces painted. The maximum number of faces, which will be painted on a smaller cube, will be three. This will happen only in the case of the smaller cubes that emerge from the corners of the big cube.  

For 2 faces to be painted, we will have to consider the smaller cubes that emerge from the edges of the big cube (leaving out the corner). So, the smaller cubes on the every edge will be (N - 2n)/n. There is a cube with an edge of 12 units in this question. 

So, the number of smaller faces with 2 faces painted = 12*(N - 2n)n

= 12*[12 - (2*4)/4]

= 12*(12 - 8)/4

= 12*(4/4)

= 12*1

= 12 

So, 12 cubes will have 2 faces painted.

Option (b) is correct.