Calculus

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.

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  1. 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%

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