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16 November, 21:02

The dimension of a rectangular shape is 5.9 by 4.1mm s measured with a veneer calliper whose minimum scale is 0.05 mm. The percentage error in its surface area is approximately.

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  1. 16 November, 21:36
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    e% = 2.2%

    Explanation:

    In the measurements it is very important the precision of the readings and the knowledge of how the uncertainty or errors in each measurement propagates when carrying out the different calculations

    In this case the area of the body is its length l = 5.9 mm, for its width a = 4.1 mm

    S = l a

    The error can be calculated using derivatives and considered the worst of all cases

    Δs = ds / dl Δl + dS / da Δa

    in this case the derivatives are very simple

    dS / dl = a

    dS / Da = l

    we substitute

    ΔS = a Δl + l Δa

    this is the absolute error

    Let's calculate its value

    Δs = 4.1 0.05 + 5.1 0.05

    Δs = 0.5 mm²

    the percentage error is this error between the magnitude of the mediated by 100

    e% = ΔS / S 100

    e% = 0.5 / (5.1 4.1) 100

    e% = 2.2%
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