Asked by Sam
The measurement of the radius of a circle is 16 inches, with a possible error of .25 inches.
Use differentials to approximate the possible propagated error in computing the area of the circle and find the percent error.
I've gotten to 2Pi*16*.25 but don't know what to do past this point.
Use differentials to approximate the possible propagated error in computing the area of the circle and find the percent error.
I've gotten to 2Pi*16*.25 but don't know what to do past this point.
Answers
Answered by
Steve
dr = .25 - the error in the radius
a = pi r^2
da = 2pi r dr
so, as you found, the variation in area is 8pi.
the relative error is thus
da/a = 8pi/(256pi) = 1/32 = 3.125%
a = pi r^2
da = 2pi r dr
so, as you found, the variation in area is 8pi.
the relative error is thus
da/a = 8pi/(256pi) = 1/32 = 3.125%
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