Question

You have a cuboid of sides 7cm, 3cm and 7cm. How many such cuboids will you need to

form a cube?​

Answer 1

Answer:

Assuming that he isn’t allowed to squish thecuboid into a cube, we need to find a combination of cuboids for which the dimensions are equal in all directions.

Let’s imagine the 7-by-7 aspect to go flat on the table, with the 3-unit dimension being the height.

Stacking two cuboids, we get 7-by-7-by-6, which is close, but not quite. Stacking further, the height grows to 9, then 12, etc. None of these match the 7, so we’ll need to think about other dimensions. If we put another stack of two cuboids next to the first stack, we’ll have 7-by-14-by-6. Put a third stack next to the first, and make each of the stacks, say, six cuboids high. Then we’ll have a shape that is 7-by-21-by-18.

What happens if the stacks are raised higher? What happens if this row is duplicated, and slip in front of the first row? And so forth…