Percent Error In Calculating The Volume
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The difference between two measurements is called a variation in the measurements. Another word for this variation - or uncertainty in measurement - is "error." error in volume of cylinder This "error" is not the same as a "mistake." It does not absolute error formula mean that you got the wrong answer. The error in measurement is a mathematical way to show the uncertainty in
Volume Error Propagation
the measurement. It is the difference between the result of the measurement and the true value of what you were measuring. The precision of a measuring instrument is determined by the smallest
Absolute Error Example
unit to which it can measure. The precision is said to be the same as the smallest fractional or decimal division on the scale of the measuring instrument. Ways of Expressing Error in Measurement: 1. Greatest Possible Error: Because no measurement is exact, measurements are always made to the "nearest something", whether it is stated or not. The greatest possible error when measuring is error in measurement physics considered to be one half of that measuring unit. For example, you measure a length to be 3.4 cm. Since the measurement was made to the nearest tenth, the greatest possible error will be half of one tenth, or 0.05. 2. Tolerance intervals: Error in measurement may be represented by a tolerance interval (margin of error). Machines used in manufacturing often set tolerance intervals, or ranges in which product measurements will be tolerated or accepted before they are considered flawed. To determine the tolerance interval in a measurement, add and subtract one-half of the precision of the measuring instrument to the measurement. For example, if a measurement made with a metric ruler is 5.6 cm and the ruler has a precision of 0.1 cm, then the tolerance interval in this measurement is 5.6 0.05 cm, or from 5.55 cm to 5.65 cm. Any measurements within this range are "tolerated" or perceived as correct. Accuracy is a measure of how close the result of the measurement comes to the "true", "actual", or "accepted" value. (How close is your answer to the accepted value?) Tolerance is the greatest range of variati
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Maximum Error Formula
hiring developers or posting ads with us Mathematics Questions Tags Users Badges Unanswered Ask Question what is maximum error _ Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join maximum possible error in measurement 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 http://www.regentsprep.org/regents/math/algebra/am3/LError.htm 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 http://math.stackexchange.com/questions/893536/what-is-the-error-in-calculated-volume-of-cylinder-given-the-measurements-of-le 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 31.4k447102 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 3484 times active 2 years ago Related 0What is the volume of a hyper cylinder in d - dimension?0Calcu
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Solutions 1. Approximations If a quantity x (eg, side of a square) is obtained by measurement and a quantity y (eg, area of the square) is calculated as a function of x, say y = f(x), then any error involved in the measurement of x produces an error in the calculated value of y as well. Recall from Section 4.3 Part 2 that the Section 8.3 Part 1, we have: That is, the error in x is dx and the corresponding approximate error in y is dy = f '(x) dx. Fig. 1.1 Fig. 1.2 – 1st and 2nd axes: if 1,000 = xa – 1 then xa = 1,001, – 1st and 3rd axes: if 1,000 = xa + 1 then xa = 999, therefore xa is somewhere in [999, 1,001]. Example 1.1 Solution Let s be the side and A the area of the square. Then A = s2. The error of the side is ds = 1 m. The approximate error of the calculated area is: dA = 2s ds = 2(1,000)(1) = 2,000 m2. EOS Note that we calculate dA from the equation A = s2, since the values of s and ds are given. To find the differential of A we must have an equation relating A to s. So even if the measured value of the side is given we still define the variable s that takes on as a value the measured value. In general, when the measured value say V of a quantity and the error say E in the measurement are given, we define a variable say x for the quantity, so that x = V and dx = E, which will be used later on in the solution. When using the quantity, first use the variable x, not the value V, then use the value V when a value is to be obtained. Go To Problems & Solutions Return To Top Of Page 2. Types Of Errors A measurement of distance d1 yields d1 = 100 m with an error of 1 m. A measurement of distance d2 yields d2 = 1,000 m with an error of 1 m. Both measurements have the same absolute error of 1 m. However, intuitively we feel that measurement of d2 has a smaller error because it's 10 times larger and yet has the same absolute error. Clearly the effect of 1 m out of 1,000 m is smaller than that of 1 m out of 100 m. This leads us to consider an error relative to the size of the quantity being expressed. This relative error is accomplished by representing the absolute error as a fraction of the quantity being expressed. For example, the relative error for d1 is 1 m / 100 m = 1/100 = 0.01 and that for d2 is 1 m / 1,000 m = 1/1,000 = 0.001. As desired the relative error for d2 is smaller than that for d1. The percentage error is the absolute error as a percentage of the quantity being expressed. For example, the percentage error for d1 is (1 m / 100 m)(100/100) = (1/100)(100)% = (0.01)(100)% = 1