If the percentage error in the radius of a ci | vedclass

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(A) Let $r$ be the radius and $A$ be the area of the circle. The area of the circle is given by $A = \pi r^2$. Taking the natural logarithm on both si

Vedclass · Accepted Answer

$6$

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(A) Let $r$ be the radius and $A$ be the area of the circle. The area of the circle is given by $A = \pi r^2$. Taking the natural logarithm on both sides, we get $\ln A = \ln \pi + 2 \ln r$. Differentiating both sides with respect to $r$, we get $\frac{dA}{A} = 2 \frac{dr}{r}$. The percentage error in the radius is given as $\frac{dr}{r} 	imes 100 = 3\%$. The percentage error in the area is $\frac{dA}{A} 	imes 100 = 2 	imes (\frac{dr}{r} 	imes 100)$. Substituting the given value, we get $\frac{dA}{A} 	imes 100 = 2 	imes 3\% = 6\%$. Thus, the percentage error in the area is $6\%$.

If the percentage error in the radius of a circle is $3\%$, then the percentage error in its area is (in $\%$)

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