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28 November, 21:51

The volume of a cylinder is V space equals space pi space r squared space h, where r is the radius of the circular faces and h is the height of the cylinder. Your measurements show that the mean value of r is 21 cm and its statistical and instrumental uncertainties turned out to be 0.10 cm and 0.20 cm, respectively. Likewise, that of h are 13 cm for the mean, 0.2 cm (statistical) and 0.3 cm (instrumental) for its uncertainties.

A. What can you say about which source of uncertainty has the largest contribution to the overall uncertainty of V?

B. What would you need to do to improve (reduce) the uncertainty on your calculation of V?

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  1. 28 November, 23:18
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    a) variable that introduces more uncertainty is the measurement of heigh

    Explanation:

    a) Uncertainty can be calculated by making differential days of volume

    V = π r² h

    the error absolute is

    ΔV = dV/dr Δr + dV/dh Δh

    ΔV = π h 2r Δr + π r² Δh

    to calculate the absolute error we use the instrument error

    ΔV = π 13 2 21 0.20 + π 21² 0.3

    ΔV = 343 + 415 = 758 cm³

    ΔV = 8 10² cm³

    To see more clearly what measurement should be performed, look for the relative error

    ΔV / V = 2 Δr / r + Δh / h

    let's use the uncertainties of the intrumetos

    ΔV / V = 2 0.2 / 21 + 0.3 / 13

    ΔV / V = 0.019 + 0.023

    let's use statistical uncertainty

    ΔV / V = 2 0.1 / 21 + 0.2 / 13

    ΔV / V = 0.0095 + 0.015

    We see that the variable that introduces more uncertainty is the measurement of height, either with the uncertainty of the instrument if a single measurement is made or with the statistical uncertainty if several measurements are made.

    b) To improve the precision of the medicines we must measure the height of the cylinder with more pressure, using an intricate that has less error.
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