Calculating Percent Uncertainty for Volume of a Beach Ball

[Melissa]

hi, I'm attempting a physics problem... it is:
What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r= 2.86 plus or minus 0.09 m.
Now, I tried to find the percent uncertainty by just doing .09/2.86, but I'm assuming I need to do something with the radius (in the way of changing it to the full volume...) before I can calculate this.
I know that to find the volume it would be 4/3 pi R cubed, but after that... how does the volume correlate to the .09? Does that need to be altered as well? I know the answer is 9% but I would like to actually understand how the question is done!
I'm just confused. Any help would be greatly appreciated!

 

[Gokul43201]

General Rule : When quantities multiply, the relative errors in those quantities add up.

The volume is proportional to the cube of the radius. As a result the percent error in volume is thrice the percent error in the radius.

 

[Melissa]

ok... so since I cube the radius, I multiply the % error by 3...
ah. and that gives me 9%.
You are a genius. Why must physics profs supply us with pages and pages of calculations when you can solve a problem like THAT instead...
Thanks :)

 

[Chronos]

apply the error propagation formula. try this link
http://www.chem.hope.edu/~polik/Chem345-2000/errorpropagation.htm