Question

. A cube is formed of 216 smaller cubes. If the longer cube is cut across both of its diagonals, then how many smaller cubes will be cut ?
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Answer 1

Answer:

66 smaller cubes will be cut.

Step-by-step explanation:

A cube is formed of 216 smaller cubes so the big cube will have a dimension of 6*6*6.

Now, the cube is cut across both of its diagonals.

The following things can be concluded:

• When cut across the first diagonal, it will cut a total of 6*6 = 36 small cubes.

• Similarly, when cutting across the second diagonal,  it will give 6*6 = 36 small cubes.

• Now, we have 6 cubes common for both the diagonals at the center.  So we will consider those 6 cube in the middle only once for any one of diagonal.

Therefore,  

Total no. of smaller cubes =  (6*6) + (6*6) – 6 = 36 + 36 – 6 = 66.