Final answer:
Teddy needs 24cm³ more small cubes to fill the box completely. The dimensions of the other box can be any dimensions that have the same volume as the first box, which is 168cm³.
Step-by-step explanation:
To calculate the volume of the small cubes, we need to find the volume of one cube and then multiply it by the total number of cubes. The volume of a cube is found by multiplying the length of one side by itself twice. In this case, the volume of one small cube is 1cm x 1cm x 1cm = 1cm³. Since Teddy has 144 small cubes, the total volume of all the cubes is 144cm³.
To find the number of more small cubes Teddy needs to fill the box completely, we need to calculate the volume of the box. The volume of a rectangular box is found by multiplying its length by its width and its height. In this case, the volume of the box is 7cm x 6cm x 4cm = 168cm³.
To find the number of more small cubes Teddy needs, we subtract the volume of the small cubes he already has from the volume of the box. So, Teddy needs 168cm³ - 144cm³ = 24cm³ more small cubes to fill the box completely.
The dimensions of the other box can be any dimensions that have the same volume as the first box, which is 168cm³. For example, the dimensions could be 4cm x 7cm x 6cm or 2cm x 12cm x 7cm, as long as the product of the three dimensions is 168cm³.