The measurement of the circumference of a circle is found to be 70 centimeters, with a possible error of 0.9 centimeter.

Question

a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places.)

b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 5%. (Round your answer to one decimal place.)

Answer 1

C = 2 pi r so r = 35/pi
so
dC = 2 pi dr
so
dr = dC/ (2 pi) = .9/(2pi)

a = pi r^2
da = 2 pi r dr
da = 70 pi dr
da/a = 70 pi dr/a
multiply by 100 to get percent