Question

The sides of a small rectangular box are measured to be 1.45 ± 0.03 cm, 2.30 ± 0.04 cm, and 3.4 ± 0.2 cm long. Calculate its volume and uncertainty in cubic centimeters. (Note that uncertainties should be reported to one significant figure.)

volume_________cm3

uncertainty_______cm3

Answer 1

Solution: Average volume can be calculated as:

1.45*2.30*3.4 = 11.34 cm³.

% uncertainity related to each sides:

For, (1.45 ± 0.03 cm) = (0.03/1.45)*100 = 2.068 %

For, (2.30 ± 0.04 cm) = (0.04/2.30)*100 = 1.74 %

For, (3.4 ± 0.2 cm) = (0.2/3.4)*100 = 5.88 %

% Volumetric uncertainity is calculated as the sum of each dimension's % uncertainity.

=> Volumetric uncertainity = 2.068 + 1.74 + 5.88 = 9.69 %.

=> Uncertainity in volume = 9.69*11.34/100 = 1.098 cm^3. Answer

And, volume = 11.34 ± 1.098 cm^3. Answer