Question

The rectangular prism below is labeled with its measured dimensions. Taking measurement error into account, what are the minimum and maximum possible volumes?

15 yd
2 yd
3 yd


Minimum possible volume =
yd³

Maximum possible volume =
yd³

Answer 1

To find the minimum and maximum possible volumes of the rectangular prism, we need to consider the measurement error for each dimension.

Given dimensions:
- Length (L) = 15 yd
- Width (W) = 2 yd
- Height (H) = 3 yd

Assuming the error is ±0.5 yd for each measurement (just as an example of a common measurement error), we can calculate the minimum and maximum dimensions as follows:

1. **Length (L)**:
- Minimum = \(15 - 0.5 = 14.5\) yd
- Maximum = \(15 + 0.5 = 15.5\) yd

2. **Width (W)**:
- Minimum = \(2 - 0.5 = 1.5\) yd
- Maximum = \(2 + 0.5 = 2.5\) yd

3. **Height (H)**:
- Minimum = \(3 - 0.5 = 2.5\) yd
- Maximum = \(3 + 0.5 = 3.5\) yd

Next, we calculate the minimum and maximum volumes:

- **Minimum Volume**:
\[
V_{\text{min}} = L_{\text{min}} \times W_{\text{min}} \times H_{\text{min}}
\]
\[
V_{\text{min}} = 14.5 \times 1.5 \times 2.5 = 54.375 \, \text{yd}^3
\]

- **Maximum Volume**:
\[
V_{\text{max}} = L_{\text{max}} \times W_{\text{max}} \times H_{\text{max}}
\]
\[
V_{\text{max}} = 15.5 \times 2.5 \times 3.5 = 136.875 \, \text{yd}^3
\]

Thus, the minimum and maximum possible volumes are:

Minimum possible volume = 54.375 yd³

Maximum possible volume = 136.875 yd³

Note: If the allowed measurement error is different, you'll need to adjust the calculations accordingly. If no specific error is given, default assumptions need to be clarified.