Final answer:
The volume of the rectangular box is 11.4 cm³, and the uncertainty in measurements would yield a small additional uncertainty to this value, which should be calculated by adding the relative uncertainties and applying them to the volume.
Step-by-step explanation:
To calculate the volume of a rectangular package, we use the formula V = lwh, where l represents the length, w the width, and h the height of the rectangle. Given the measurements of a small rectangular box having sides 1.80 cm, 2.05 cm, and a height of 3.1 cm, the volume can be calculated by multiplying these dimensions: V = 1.80 cm × 2.05 cm × 3.1 cm. To find the uncertainty in the volume calculated, we consider the uncertainty in each measurement and propagate it through the multiplication using the approximation that the relative uncertainties add when multiplied.
The volume of the given rectangular box is thus:
- V = 1.80 cm × 2.05 cm × 3.1 cm = 11.439 cm³, or approximately 11.4 cm³.
The uncertainties of the individual measurements are ±0.01 cm, ±0.02 cm, and ±0.1 cm for length, width, and height respectively. By adding these relative uncertainties, which would be a small percentage of the respective side's measurement, we can estimate the uncertainty in the volume. The student should use proper significant figures based on the uncertainty in the measurements for the final reported volume.