Question

What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r =

(0.84 ± 0.04) m?

Answer 1

The uncertainty can be found from the following equation:

$$V=\frac43\pi R^3=2.48\text{ m}^3.\\\space\\\frac{\Delta V}{V}=3\frac{\Delta R}{R},\\\space\\ \Delta V=3V\frac{\Delta R}{R}=0.35\text{ m}^3.$$