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In measuring the circumference of a circle, there is an error of 0.05 cm. If with this error the circumference of the circle is measured as C cm, then the error in area is

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a

$\frac{0.025 C}{π} sq . cm$

b

$\frac{0.25 C}{π} sq . cm$

c

$\frac{0.0025 C}{π} sq . cm$

d

$\frac{25 C}{π} sq . cm$

answer is A.

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Detailed Solution

$\begin{array}{rcl} δP & = & 0.05 p = c \\ A & = & {πr}^{2} p = 2 πr \Rightarrow r = \frac{p}{2 π} \\ A & = & π (\frac{p^{2}}{4 {πr}^{2}}) = \frac{p^{2}}{4 π} \Rightarrow δA = \frac{2 pδp}{4 π} = \frac{c (0.05)}{2 π} \\ = & \frac{0.025}{π} \end{array}$

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