Question

how do you find the approximate uncertainty, of a sphere of radius 1.96 ± 0.01 m?

the Volume is 31.5

Answer 1

the relative uncertainty in the radius, i.e. 0.01/1.96,
should be equal to the uncertainty in the volume ?/31.5

Answer 2

@UnkleRhaukus

Because the value for radius is cubed (^3) I believe the uncertainty in volume is 3 times uncertainty in radius

Answer 3

@svaquero1 There are several ways you could find the uncertainty in the Volume. The easiest to understand is to calculate of volume with the radius + the uncertainty in the radius to get the largest volume you might expect . Then calculate the volume with the radius - the uncertainty in the radius to get the smallest volumes you might expect. Take the difference of those volumes and divide by two. the result is the uncertainty in the volume, v
\[Volume \pm v\]

Answer 4

Please apply this rule:
\[\frac{ \Delta V}{ V }=3\frac{ \Delta R }{ R }\]
where: Delta R is the uncertainty on the radius R,
Delta V is the uncertainty on the Volume V,
V is the Volume of your sphere, and R is the radius of your sphere