CALCULUS QUESTION!

Question

The measurement of the circumference of a circle is found to be 70 centimeters, with a possible error of 0.9 centimeter.
(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=70=2Πr                  Please excuse the awkward symbol for pi!

dC=0.9=2Πdr

r=35/Π

dr = 0.45/Π

 

A=Πr²
 =Π(35/Π)² = 1225/Π

dA=2Πr(dr)

    = 2Π(35/Π)(0.45/Π) = 70(0.45)/Π = 31.5/Π

 

dA/A = 31.5/Π ÷  1225/Π = 9/350 = 0.0257 = 2.57%  is the Approximate percent error in computing the area of the circle.