Maths-
General
Easy

Question

If there is an error of 0.02 sq. cm is made in calculating the area of a circle. If the radius is 5cm, then the percentage error in the circumference of the circle is

  1. fraction numerator 0.4 over denominator pi end fraction    
  2. fraction numerator 0.04 over denominator pi end fraction    
  3. fraction numerator 4 over denominator pi end fraction    
  4. fraction numerator 0.004 over denominator pi end fraction    

Hint:

% error in the circumference of the circle = fraction numerator delta C over denominator C end fraction space cross times 100

The correct answer is: fraction numerator 0.04 over denominator pi end fraction


     Given : 
    delta A space equals space 0.02 space comma space r space equals space 5 c m
    Area of circle(A) = πr squared
    delta A space equals space fraction numerator d A over denominator d r end fraction space cross times delta r
    Differentiating 'A' w.r.t 'r'
    fraction numerator d A over denominator d r end fraction equals straight pi dr squared over dr equals space 2 πr space
    delta A space equals space fraction numerator d A over denominator d r end fraction space cross times delta r
    0.02 = 2 πr space cross times space δr
    delta r space equals space fraction numerator 0.02 over denominator 2 straight pi space cross times 5 end fraction space equals space fraction numerator 0.002 over denominator straight pi end fraction
    Circumference of circle(C) = 2 πr
    C = 2 cross times straight pi space cross times 5
    C = 10straight pi
    delta C space equals space fraction numerator d C over denominator d r end fraction cross times delta r
    Differentiating 'C' w.r.t 'r'
    delta C space equals fraction numerator d C over denominator d r end fraction cross times delta r
fraction numerator d C over denominator d r space end fraction space equals space 2 straight pi space cross times dr over dr equals space 2 straight pi
δC space equals 2 straight pi cross times fraction numerator 0.002 over denominator straight pi end fraction space equals space 0.004
    % error in the circumference of the circle = fraction numerator delta C over denominator C end fraction space cross times 100
    % error in the circumference of the circle  = fraction numerator 0.004 over denominator 10 straight pi end fraction cross times 100 = fraction numerator 0.04 over denominator straight pi end fraction

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