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:
-
Length (L):
- Minimum = \(15 - 0.5 = 14.5\) yd
- Maximum = \(15 + 0.5 = 15.5\) yd
-
Width (W):
- Minimum = \(2 - 0.5 = 1.5\) yd
- Maximum = \(2 + 0.5 = 2.5\) yd
-
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.
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