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How do you figure out the percent uncertainty in the volume of a sphere when you know its radius with a particular degree of certainty?

Asked by HeroicZach (195points) August 25th, 2009

I’m looking to figure out the percent uncertainty in the volume of a sphere with known radius. The radius itself has a particular degree of certainty…it looks like this: 2.86 ± .09m. How do I turn that known uncertainty into a percent uncertainty for the volume of the entire sphere, not just the radius figure itself?

Full disclosure: yes, this is on my homework, no, I am not asking you to do this for me, OK? Explanations and whatever help you can offer would be great =)

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