Question

In measuring the internal radius of a circular sewer the measurement is 2% too large. If this measurement is then used to calculate the circular cross-sectional area of the pipe: Determine, by using the binomial theory, the percentage error that will occur compared to the true area.

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Clarabelle

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68 Answers

area of cross section is pie(r)^2; now error is 2% whixh is 0.02;
now radius is r+0.02r=1.02r;
now area of cross section is pie(1.02r)^2= 1.0404r^2;
%error = (area - truearea)/truearea * 100
= (pie * 1.0404r^2 - pie * r^2)/pie(r^2) *100
=4.04% error

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