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(C) Given the circumference of a circle $S = 2 \pi r = 56 	ext{ cm}$.From this,the radius $r = \frac{56}{2 \pi} = \frac{28}{\pi} 	ext{ cm}$.The erro

Vedclass · Accepted Answer

$1/14$

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(C) Given the circumference of a circle $S = 2 \pi r = 56 	ext{ cm}$.From this,the radius $r = \frac{56}{2 \pi} = \frac{28}{\pi} 	ext{ cm}$.The error in circumference is given by $\delta S = 2 \pi \delta r = 0.02 	ext{ cm}$.Thus,$\delta r = \frac{0.02}{2 \pi} 	ext{ cm}$.The area of the circle is $A = \pi r^2$.The relative error in area is given by $\frac{\delta A}{A} = 2 \frac{\delta r}{r}$.Substituting the values:$\frac{\delta A}{A} = 2 	imes \frac{\frac{0.02}{2 \pi}}{\frac{28}{\pi}} = 2 	imes \frac{0.02}{2 \pi} 	imes \frac{\pi}{28} = \frac{0.02}{28} = \frac{2}{2800} = \frac{1}{1400}$.The percentage error is $\frac{\delta A}{A} 	imes 100 = \frac{1}{1400} 	imes 100 = \frac{1}{14} \%$. Therefore,the percentage error in the area is $1/14 \%$.

The circumference of a circle is measured as $56 \text{ cm}$ with an error of $0.02 \text{ cm}$. The percentage error in its area is

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