the rectangular prism below is labeled with its measured dimensions. taking measurement error into account…

Explanation:

Step1: Calculate the nominal volume

The volume formula for a rectangular - prism is $V = l\times w\times h$. Here, $l = 12$ m, $w = 16$ m, and $h = 19$ m. So, $V_{nominal}=12\times16\times19=3648$ m³.

Step2: Consider measurement error

Assume the measurement error for each dimension is $\pm0.5$ m. The maximum - volume occurs when we take the maximum values of each dimension: $l_{max}=12 + 0.5=12.5$ m, $w_{max}=16 + 0.5=16.5$ m, $h_{max}=19+0.5 = 19.5$ m. Then $V_{max}=12.5\times16.5\times19.5 = 12.5\times321.75=4021.875$ m³. The minimum - volume occurs when we take the minimum values of each dimension: $l_{min}=12 - 0.5 = 11.5$ m, $w_{min}=16 - 0.5=15.5$ m, $h_{min}=19 - 0.5 = 18.5$ m. Then $V_{min}=11.5\times15.5\times18.5=11.5\times286.75 = 3307.625$ m³. The greatest deviation from the nominal volume is $\Delta V=\max{|V_{max}-V_{nominal}|,|V_{min}-V_{nominal}|}$. $|V_{max}-V_{nominal}|=4021.875 - 3648=373.875$ m³. $|V_{min}-V_{nominal}|=3648 - 3307.625 = 340.375$ m³. So, $\Delta V = 373.875$ m³.

Step3: Calculate percent error

The percent - error formula is $\text{Percent Error}=\frac{\Delta V}{V_{nominal}}\times100%$. $\text{Percent Error}=\frac{373.875}{3648}\times100%\approx10.2%$.

Answer:

$10.2%$