To calculate the minimum and maximum possible volumes of a rectangular prism while considering measurement error, we'll need to assume there's some tolerance in the measurement of each of the dimensions (length, width, and height).

Since you didn't provide specific measurement errors, I'll give you a general process you can follow. Here's how to proceed:

1. Determine the nominal volume:

The nominal volume of a rectangular prism is simply the product of its three dimensions.

$V = \text{Length} \times \text{Width} \times \text{Height}$ Given the dimensions $6 \, \text{cm}, 15 \, \text{cm}, 12 \, \text{cm}$:

$V = 6 \times 15 \times 12 = 1080 \, \text{cm}^3$

2. Account for possible measurement errors:

To account for error, the minimum volume occurs when each dimension is at its smallest possible value (reduced by the error margin), and the maximum volume occurs when each dimension is at its largest possible value (increased by the error margin).

For example, if each dimension has a possible error of $\pm \delta$, the dimensions could vary from:

• Length: $6 - \delta$ to $6 + \delta$
• Width: $15 - \delta$ to $15 + \delta$
• Height: $12 - \delta$ to $12 + \delta$

Minimum Volume:

$V_{\text{min}} = (6 - \delta) \times (15 - \delta) \times (12 - \delta)$

Maximum Volume:

$V_{\text{max}} = (6 + \delta) \times (15 + \delta) \times (12 + \delta)$

3. Interpretation:

To complete this process, you would need to know the actual error margin $\delta$. Once you have that, you can substitute it into the formulas to compute the minimum and maximum volumes.

Do you have a specific measurement error or tolerance for each of the dimensions? If so, I can help you with the exact calculation!