Question

What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 0.94 ±0.06 m ?

Express your answer using two significant figures.

Answer 1

$\large Volume = \frac{4}{3}\pi r^{3}$

Taking log both side and differentiate it we get

$\frac{\Delta V}{V} =3\frac{\Delta R}{R}\\\ \frac{\Delta V}{V}= 3*\frac{0.06}{0.94} \\ \frac{\Delta V}{V} = 0.1914\\ \frac{\Delta V}{V} =19\ percent$

=19%