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Volume Error Propagation

_ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join how to calculate percent error in volume them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What is the error in calculated volume

Maximum Error Formula

of cylinder, given the measurements of length and radius? up vote -2 down vote favorite Measured length of the rod is $15 \pm 0.4$ cm and the radius of the rod is $6.1 \pm 0.2$ cm. What is the error in calculated volume? (two decimal places) What i've tried is $$V=\pi r^2 l$$ $$V=1753.48 \text{ cm}^3$$ $$DV/ 1753.48= 2(0.2/6.1) + (0.4)/15$$ $$DV = 161.74 \text{ cm}^3$$ But I got it wrong. geometry volume error-propagation share|cite|improve this question uncertainty calculator edited Aug 11 '14 at 2:21 user147263 asked Aug 11 '14 at 0:03 user161853 712 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote $V(r,l)=\pi r^2l$, so \begin{align} V(r+\Delta r,l+\Delta l)&\approx V(r,l)+\frac{\partial V}{\partial r}\Delta r+\frac{\partial V}{\partial l}\Delta l\\ &\approx V(r,l)+2\pi r l\Delta r+\pi r^2\Delta l \end{align} So error in $V$ is $2\pi r l\Delta r+\pi r^2\Delta l$. Note this does not factor in statistics/probability. If the given information is meant to convey that $l$ has a Normal distribution centered at $15$ with $\sigma=0.4$, and that $r$ has a Normal distribution centered at $6.1$ with $\sigma=0.2$, then $\Delta V$ should be computed as $$\sqrt{\left(2\pi r l\Delta r\right)^2+\left(\pi r^2\Delta l\right)^2}$$ share|cite|improve this answer edited Aug 11 '14 at 0:39 answered Aug 11 '14 at 0:13 alex.jordan 31.2k447102 add a comment| Your Answer draft saved draft discarded Sign up or log in Sign up using Google Sign up using Facebook Sign up using Email and Password Post as a guest Name Email Post as a guest Name Email discard By posting your answer, you agree to the privacy policy and terms of service. Not the answer you're looking for? Browse other questions tagged geometry volume error-propagation or ask your own question. asked 2 years ago viewed 3125 times active 2 years ago Get the weekly newsletter! In it, you'll get: The week's top questions and ans

Treatments MSDS Resources Applets General FAQ Uncertainty ChemLab Home Computing Uncertainties in Laboratory Data and Result This section considers the error and uncertainty in experimental measurements and calculated results. First, here are some fundamental things you should realize about

Error In Measurement Physics

uncertainty: • Every measurement has an uncertainty associated with it, unless it is

Systematic Error

an exact, counted integer, such as the number of trials performed. • Every calculated result also has an uncertainty, related to absolute error the uncertainty in the measured data used to calculate it. This uncertainty should be reported either as an explicit ± value or as an implicit uncertainty, by using the appropriate number of significant figures. http://math.stackexchange.com/questions/893536/what-is-the-error-in-calculated-volume-of-cylinder-given-the-measurements-of-le • The numerical value of a "plus or minus" (±) uncertainty value tells you the range of the result. For example a result reported as 1.23 ± 0.05 means that the experimenter has some degree of confidence that the true value falls in between 1.18 and 1.28. • When significant figures are used as an implicit way of indicating uncertainty, the last digit is considered uncertain. For example, a https://www.dartmouth.edu/~chemlab/info/resources/uncertain.html result reported as 1.23 implies a minimum uncertainty of ±0.01 and a range of 1.22 to 1.24. • For the purposes of General Chemistry lab, uncertainty values should only have one significant figure. It generally doesn't make sense to state an uncertainty any more precisely. To consider error and uncertainty in more detail, we begin with definitions of accuracy and precision. Then we will consider the types of errors possible in raw data, estimating the precision of raw data, and three different methods to determine the uncertainty in calculated results. Accuracy and Precision The accuracy of a set of observations is the difference between the average of the measured values and the true value of the observed quantity. The precision of a set of measurements is a measure of the range of values found, that is, of the reproducibility of the measurements. The relationship of accuracy and precision may be illustrated by the familiar example of firing a rifle at a target where the black dots below represent hits on the target: You can see that good precision does not necessarily imply good accuracy. However, if an instrument is well calibrated, the precision or reproducibility of the result is a good measure of it

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