Question

which shows how find the volume of this prism?

5 + 12 + 6 = 23 cm 3
5 x 12 = 60 cm 3
5 x 12 x 6 = 360 cm 3
(5 x 12) x 12 = 720 cm 3

Answer 1

To find the volume of a prism, you typically use the formula:

\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]

From your calculations, it looks like you're working with a rectangular prism where the dimensions are given (though it's not entirely clear what each number represents). Let's break down the numbers you provided:

1. **Base Area Calculation**:
- The base dimensions you mentioned seem to be 5 cm and 12 cm, so you calculated the area of the base as:
\[
5 \times 12 = 60 \, \text{cm}^2
\]
- This is correct for the base area.

2. **Volume Calculation**:
- If the height of the prism is 6 cm, then the volume of the prism would be:
\[
\text{Volume} = \text{Base Area} \times \text{Height} = 60 \, \text{cm}^2 \times 6 \, \text{cm} = 360 \, \text{cm}^3
\]
- This aligns with your calculation of \(5 \times 12 \times 6 = 360 \, \text{cm}^3\).

3. **Other Calculations**:
- The first line \(5 + 12 + 6 = 23 \) does not relate to volume, as volume involves multiplication, not addition.
- The calculation \( (5 \times 12) \times 12 = 720 \, \text{cm}^3\) is also incorrect in the context of a standard prism volume; it seems to double one of the dimensions.

### Conclusion:
- The volume of the rectangular prism, using the base dimensions of 5 cm by 12 cm and height of 6 cm, is **360 cm³**.
- The proper formula to remember is:
\[
\text{Volume} = \text{Base Length} \times \text{Base Width} \times \text{Height}
\] where for this prism, it would be \(5 \times 12 \times 6\).