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%
The measurement of the radius of a circle is 16 inches, with a possible error of .25 inches.
Use differentials to approximate the possible propagate error in computing the area of the circle.
2 answers
a = pi r^2
da = 2pi r dr
now just plug in your numbers.
da = 2pi r dr
now just plug in your numbers.
1 answer