Question

A solid cube of size 4" is cut into smaller cubes of ,1" and 2" dimensions. If the number of 1" and 2" cubes are multiples of 7, what
will be the total number of smaller cubes (of all size together)?​

Answer 1

Answer:

22 cubes are formed of all sizes.

Explanation:

First, count the total number of possible 2'' cubes. We get 8.

However, 8 is not a multiple of 7. The only multiple of 7 that is less than 8 is 7. Hence, there are 7 of 2'' cubes.

Now, we are left with one 2'' cube to work with. This two inch cube can be divided into 8 one inch cubes. Again, 8 is not a multiple of 7, hence we can say that there are 7 of 1 '' cubes.

Lastly, we are left with one 1'' cube. This cube can be divided into 8  ¹/₂'' cubes. Hence there are 8 ¹/₂'' cubes.

Altogether, we have 7 + 7 + 8 = 22 cubes in all.