Uncertainty, volume, and measurement

[mncyapntsi]

Homework Statement

Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...

Relevant Equations

v=3pi/4r^3

I have done this question and gotten:

Vmin = 4pi/3(19.18)^3=29555.2
V = 4pi/3(19.31)^3=30160.3
Vmax = 4pi/3(19.44)^3=30773.5

Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04% however this is wrong...
Could someone please help me find out where I went wrong, or tell me if I went the wrong direction? I was told I should apparently be using calculus to solve this, but I have no clue where to even start...
Any help would be much much appreciated!

Have a wonderful day

 

[PeroK]

How is the uncertainty defined?

 

[jbriggs444]

Homework Statement:: Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...

Does this amount to an absolute uncertainty of 0.13 or 0.26?

Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04%

You may or may not have received guidance about significant figures in reports of uncertainty. It is almost never appropriate to report uncertainty to more than two significant figures.

 

[bob012345]

Homework Statement:: Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...
Relevant Equations:: v=3pi/4r^3

I have done this question and gotten:

Vmin = 4pi/3(19.18)^3=29555.2
V = 4pi/3(19.31)^3=30160.3
Vmax = 4pi/3(19.44)^3=30773.5

Uncertainty: {[30773.5-29555.2]/30160.3}x100=4.04% however this is wrong...
Could someone please help me find out where I went wrong, or tell me if I went the wrong direction? I was told I should apparently be using calculus to solve this, but I have no clue where to even start...
Any help would be much much appreciated!

Have a wonderful day

Have you taken calculus yet? Are you familiar with derivatives? Also, why do you think you are wrong?

 

[haruspex]

Homework Statement:: Find the % uncertainty of the V of a sphere with r = 19.31 plus or minus 0.13...

I should apparently be using calculus to solve this

Note the "plus or minus". How does that compare with your answer of 4%?

You can use calculus. It leads to a useful general result about how small fractional errors in a linear dimension translate into fractional errors in two and three dimensions. But for the purpose of this question, your method is fine.