Relative Uncertainty

Length and Volume

What is the relative uncertainty in the following:

a) 3.26+.25m

b) The volume of a sphere with a radius r=2.86 +/- 0.08 m

a) relative uncertainty: 0.25/3.26 = 0.077 = 7.7%

b) V=4/3 pi r³

DeltaV/V=4/3 3 (Delta r) pi *r²/(4/3 pi r³)
= 3 Delta r/r

= 8.4%