The sides of a small rectangular box are measured to be 1.80±0.01cm1.80±0.01cm , 2.05±0.02cm, and 3.1±0.1 cm2.05±0.02cm, and 3.1±0.1 cm long. Calculate its volume and uncertainty in cubic centimeters.

The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

First, calculate the volume: V = 1.80 cm * 2.05 cm * 3.1 cm = 11.37 cm³

Next, calculate the uncertainty. The uncertainty in a product or quotient is given by the sum of the relative uncertainties of each measurement.

The relative uncertainty of each measurement is the absolute uncertainty divided by the measurement itself.

Relative uncertainty in length = 0.01 cm / 1.80 cm = 0.00556 Relative uncertainty in width = 0.02 cm / 2.05 cm = 0.00976 Relative uncertainty in height = 0.1 cm / 3.1 cm = 0.03226

Add these relative uncertainties to find the total relative uncertainty: Total relative uncertainty = 0.00556 + 0.00976 + 0.03226 = 0.04758

Finally, multiply the volume by the total relative uncertainty to find the absolute uncertainty in the volume: Uncertainty in volume = V * total relative uncertainty = 11.37 cm³ * 0.04758 = 0.54 cm³

So, the volume of the box is 11.37 ± 0.54 cm³.