What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 0.84 ± 0.04m ?

Answer 1

v = (4/3) pi r^3

dv/dr = 4 pi r^2
(which is the surface area of course :)

dv = 4 pi r^2 dr
dv/v = 4 pi r^2 dr/(4/3)pir^3

dv/v = 3 dr/r
here dr = .04
and r = .84
so 100 * 3 dr/r = 12/.84 = 14.3 %

Answer 2

how do u get dv/v = 3 dr/r ?