Question

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

a) Volume: 11.28 cm³, Uncertainty: 0.43 cm³
b) Volume: 11.28 cm³, Uncertainty: 0.19 cm³
c) Volume: 11.28 cm³, Uncertainty: 0.1 cm³
d) Volume: 11.28 cm³, Uncertainty: 0.44 cm³

Answer 1

To calculate the volume of the rectangular box, multiply the lengths of its sides. The volume is 11.28 cm³ with an uncertainty of 0.43 cm³. Hence, a) is correct.

Step-by-step explanation:

To calculate the volume of the rectangular box, you need to multiply the lengths of its sides. The length, width, and height of the box are measured to be 1.80±0.01 cm, 2.05±0.02 cm, and 3.1±0.1 cm, respectively. To find the volume, you multiply these values together: (1.80 cm) x (2.05 cm) x (3.1 cm) = 11.1285 cm³. Rounding to the correct number of significant figures gives a volume of 11.28 cm³.

The uncertainty in the volume is calculated by finding the maximum possible volume and subtracting the minimum possible volume. The maximum volume occurs when all the measurements are at their upper limits, and the minimum volume occurs when all the measurements are at their lower limits. So, the uncertainty in the volume is (2.85 cm³ - 10.90 cm³) = 0.43 cm³.