Question
Raymond used 42 cubes to build the first layer of a rectangular prism the edge length of each cube was 1 inch the finished prism had a total of 7 layers what is the volume of Raymond prism in cubic inches
Answers
GPT-4o mini
To find the volume of Raymond's rectangular prism, we first calculate the volume of one layer and then multiply that by the number of layers.
1. **Volume of One Layer:**
Each layer is made up of 42 cubes, and since each cube has a volume of \(1 \text{ inch}^3\) (because its edge length is 1 inch), the volume of one layer is:
\[
\text{Volume of one layer} = 42 \text{ cubes} \times 1 \text{ inch}^3/\text{cube} = 42 \text{ inches}^3
\]
2. **Total Volume of the Prism:**
The prism has a total of 7 layers. Therefore, the total volume of the prism is:
\[
\text{Total Volume} = \text{Volume of one layer} \times \text{Number of layers} = 42 \text{ inches}^3 \times 7 = 294 \text{ inches}^3
\]
Thus, the volume of Raymond's prism is \(\boxed{294}\) cubic inches.
1. **Volume of One Layer:**
Each layer is made up of 42 cubes, and since each cube has a volume of \(1 \text{ inch}^3\) (because its edge length is 1 inch), the volume of one layer is:
\[
\text{Volume of one layer} = 42 \text{ cubes} \times 1 \text{ inch}^3/\text{cube} = 42 \text{ inches}^3
\]
2. **Total Volume of the Prism:**
The prism has a total of 7 layers. Therefore, the total volume of the prism is:
\[
\text{Total Volume} = \text{Volume of one layer} \times \text{Number of layers} = 42 \text{ inches}^3 \times 7 = 294 \text{ inches}^3
\]
Thus, the volume of Raymond's prism is \(\boxed{294}\) cubic inches.