Question

The sides of a small rectangular box are measured to be 1.50 ± 0.01 cm, 2.05 ± 0.06 cm, and 3.8 ± 0.1 cm long. Calculate its volume and uncertainty in cubic centimeters. (Express your answers to the correct number of significant figures and proper units.)

volume  in cm³

uncertainty in cm³

Answer 1

The volume is

$$V_v=abc=1.5·2.05·3.8=11.7\text{ cm}^3.$$

The uncertainty:

$$\Delta V=\\=\sqrt{(1.50·2.05·0.1)^2+(2.05·3.8·0.01)^2+(1.50·3.8·0.06)^2}=\\ =0.5\text{ cm}.$$

$$V=V_v\pm\Delta V=(11.7\pm0.5)\text{ cm}^3$$