- #1
Coop
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Homework Statement
Hello,
I have solved the problem, but not the way the writer intended. I need help figuring out how they wanted me to do it.
Here's the problem:
The circumference of a sphere is found to be 0.98 m +/- 0.01 m. Calculate the volume and absolute error with five digits to the right of the decimal.
Homework Equations
C = 2∏r
V = (4/3)∏r3
The Attempt at a Solution
I used the low end (.97 m) and high end (.99 m) circumference measurement to solve for two radii. Then I plugged those into the volume equation and got to volume values: .01541 m3 and .01639 m3. Averaging those volumes I found the final volume to be .01589 m3.
To find the absolute uncertainty I merely subtracted the high end circumference value from the low end one and divided by two.
∴ volume = .01589 m3 +/- .00049 m3.
But my question is, they wanted me to find absolute uncertainty using the following formulas:
Δ[constant]X = [constant]*ΔX to account for constants
(Δtotal/final value) = |n| * [(ΔX)/X] to find uncertainty values where n is an exponent on A
ΔX = [(ΔX)/X] * X to convert from relative to absolute error
...where Δ stands for uncertainty
How would I do this?
It seems a lot more confusing for no reason, but would there be any case when I wouldn't be able to use my method and would have to use these formulas?
P.S. Is there anyway to code when writing these? Like I know for some help sites you can input fractions using commands like \frac{num.}{denom.}