To determine the volume of a rectangular prism, you can use two different approaches, both of which will yield the same result. Here’s how you can do it:
### Approach 1: Direct Calculation Using Length, Width, and Height
1. Identify the dimensions of the rectangular prism:
- Length (L) = 7 inches
- Width (W) = 5 inches
- Height (H) = 10 inches
2. Use the volume formula for a rectangular prism:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
3. Substitute the dimensions into the formula:
[tex]\[
\text{Volume} = 7 \, \text{inches} \times 5 \, \text{inches} \times 10 \, \text{inches}
\][/tex]
4. Calculate the volume:
[tex]\[
\text{Volume} = 350 \, \text{cubic inches}
\][/tex]
### Approach 2: Using the Base Area and Height
1. First, calculate the area of the base of the rectangular prism:
[tex]\[
\text{Base Area} = \text{Length} \times \text{Width}
\][/tex]
2. Substitute the length and width into the formula for the base area:
[tex]\[
\text{Base Area} = 7 \, \text{inches} \times 5 \, \text{inches}
\][/tex]
3. Calculate the base area:
[tex]\[
\text{Base Area} = 35 \, \text{square inches}
\][/tex]
4. Now, use the base area to find the volume of the rectangular prism:
[tex]\[
\text{Volume} = \text{Base Area} \times \text{Height}
\][/tex]
5. Substitute the base area and height into the formula:
[tex]\[
\text{Volume} = 35 \, \text{square inches} \times 10 \, \text{inches}
\][/tex]
6. Calculate the volume:
[tex]\[
\text{Volume} = 350 \, \text{cubic inches}
\][/tex]
### Conclusion
Both methods result in the same volume for the rectangular prism, which is 350 cubic inches. You can use either the direct calculation using the length, width, and height or calculate the base area first and then multiply by the height to find the volume.
