Question

The edge of a cube was found to be 1.50 plus or minus 0.05 what is its surface area and its volume.

Answer 1

1. The area is $A = 6\cdot 1.50^2 = 13.5$. The error is (see https://www.geol.lsu.edu/jlorenzo/geophysics/uncertainties/Uncertaintiespart2.html):

$$\Delta A = A\cdot 6\cdot 2\cdot \dfrac{0.05}{1.5}\approx 5$$

Thus

$$A = 14 \pm5$$

2. The volume is $V = 1.50^3 = 3.375$. The error is:

$$\Delta V = V\cdot 3\cdot \dfrac{0.05}{1.5} \approx 0.3$$

Thus, the volume is:

$$V = 3.4\pm 0.3$$