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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

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a

$\frac{0.004}{π}$

b

$\frac{0.4}{π}$

c

$\frac{0.04}{π}$

d

$\frac{4}{π}$

answer is B.

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Detailed Solution

$r = 5, δ A = 0.02 A = π r^{2} \Rightarrow δ A = 2 π r δ r \Rightarrow δ r = \frac{0.02}{2 π (5)} = \frac{0.002}{π} n o w C = 2 π r \log C = \log (2 π) + \log r \Rightarrow \frac{1}{C} δ C = 0 + \frac{1}{r} (δ r) \Rightarrow \frac{δ C}{C} \times 100 = \frac{1}{5} \times \frac{0.002}{π} \times 100 = \frac{0.04}{π}$

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