Question

Clarence is going to use one-inch cubes to make a rectangular prism. The volume of the prism will be 72 cubic inches, and Clarence wants the prism to be 3 inches tall. He also wants the length to be longer than the width. How many rectangular prisms with different dimensions could Clarence make?

Answer 1

To find the number of different rectangular prisms Clarence can make, we need to consider the factors of the given volume (72 cubic inches) and ensure that the height is fixed at 3 inches, and the length is longer than the width.

1. Start with the volume: 72 cubic inches.
2. The height is fixed at 3 inches.

Now, let's find the possible combinations for the length and width such that the length is longer than the width:

- Length can be 6 inches (2 inches longer than the height), and width can be 4 inches.
- Length can be 8 inches (4 inches longer than the height), and width can be 3 inches.

So, Clarence can make 2 different rectangular prisms with the given conditions.