Question 6
A cube, with side length $6$ cm, is to be dissected into $49$ smaller cubes. If the size of the smaller cubes does not need to be all the same but the side length, in cm, of each smaller cube must all be integers, then how many types of cubes of different sizes do we have? What is the number of cubes of each type?
Answer form: ___ types; ___ cubes of side 1 cm, ___ of side 2 cm, ___ of side 3 cm, ___ of side 4 cm, and ___ of side 5 cm.
Describe the cutting way.
Answer form: ___ types; ___ cubes of side 1 cm, ___ of side 2 cm, ___ of side 3 cm, ___ of side 4 cm, and ___ of side 5 cm.
Describe the cutting way.