build 3 different rectangular prisms with volume 12 cubic centimetres. describe each prism.
1x1x12
1x2x6
2x2x3
To build three different rectangular prisms with a volume of 12 cubic centimeters, we will vary the dimensions of each prism. Here are the descriptions of each prism:
1. Prism 1:
- Length: 2 cm
- Width: 2 cm
- Height: 3 cm
2. Prism 2:
- Length: 3 cm
- Width: 2 cm
- Height: 2 cm
3. Prism 3:
- Length: 1 cm
- Width: 4 cm
- Height: 3 cm
Each prism has different dimensions but the same volume of 12 cubic centimeters. These variations in dimensions result in different shapes and proportions for the rectangular prisms.
To build three different rectangular prisms with a volume of 12 cubic centimeters, you need to consider various combinations of length, width, and height. The different prisms can have different dimensions as long as their volumes remain the same.
Let's explore three different possibilities:
1. Prism 1:
- Length: 2 cm
- Width: 3 cm
- Height: 2 cm
To calculate the volume, multiply the length, width, and height: Volume = 2 cm x 3 cm x 2 cm = 12 cubic centimeters.
So, the first rectangular prism has dimensions of 2 cm by 3 cm by 2 cm.
2. Prism 2:
- Length: 1 cm
- Width: 6 cm
- Height: 2 cm
Volume = 1 cm x 6 cm x 2 cm = 12 cubic centimeters.
Therefore, the second rectangular prism has dimensions of 1 cm by 6 cm by 2 cm.
3. Prism 3:
- Length: 4 cm
- Width: 1 cm
- Height: 3 cm
Volume = 4 cm x 1 cm x 3 cm = 12 cubic centimeters.
Hence, the third rectangular prism has dimensions of 4 cm by 1 cm by 3 cm.
These are just three examples, but with different combinations of length, width, and height, you can create numerous rectangular prisms with a volume of 12 cubic centimeters.