Ben has 4 unit cubes how many rectangular prisms can he make using all 4 unit cubes
Can he make a 2 by 2, and a 1 by 4??
2 prisms
To determine the number of rectangular prisms that can be formed using 4 unit cubes, we need to consider the possible dimensions of the rectangular prisms.
A rectangular prism is defined by its length, width, and height. Since we have 4 unit cubes, we can arrange them in different ways to form rectangular prisms.
Let's consider the possible dimensions:
1. Length, Width, and Height of 1 unit each: In this case, we use only one cube, and we can arrange the 4 cubes in 4 different ways.
2. Length and Width of 1 unit each, and Height of 2 units: In this case, we use two cubes to form the height, and we can arrange the remaining 2 cubes in 2 different ways.
3. Length and Width of 1 unit each, and Height of 4 units: In this case, we use all 4 cubes to form the height, and there is only one arrangement.
4. Length and Width of 2 units each, and Height of 1 unit: In this case, we use two cubes to form both the length and width, and we can arrange the remaining 2 cubes in 2 different ways.
5. Length and Width of 2 units each, and Height of 2 units: In this case, we use two cubes to form both the length and width, and we use the remaining 2 cubes to form the height. There is only one arrangement.
6. Length of 2 units, Width of 1 unit, and Height of 4 units: In this case, we use two cubes for the length, one cube for the width, and one cube for the height. There is only one arrangement.
7. Length of 4 units, Width of 1 unit, and Height of 1 unit: In this case, we use all 4 cubes for the length, and there is only one arrangement.
Adding up all the possibilities, we find that Ben can make a total of 13 different rectangular prisms using the 4 unit cubes.