4
Chat with our AI personalities
8
4
To find the number of different rectangular prisms that can be built using 18 unit cubes, we need to determine the possible dimensions ( (l, w, h) ) such that ( l \times w \times h = 18 ), where ( l ), ( w ), and ( h ) are positive integers. The factor combinations of 18 are: ( (1, 1, 18) ), ( (1, 2, 9) ), ( (1, 3, 6) ), ( (2, 3, 3) ), and their permutations. Counting unique arrangements, there are a total of 6 distinct rectangular prisms that can be formed.
To determine the number of different rectangular prisms that can be made using exactly 12 cubes, we need to find all the possible combinations of dimensions that result in a volume of 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. Each factor represents a possible dimension for the rectangular prism. Therefore, there are 6 different rectangular prisms that can be made using exactly 12 cubes.
There are many options: 2 rectangular prisms 2 cubes 2 parallelepipeds 2 tetrahedrons 2 square based pyramids are some possibilities using convex polyhedra.