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Provide solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise  multiple choice question 12

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Answer: \frac{1}{14}%

Hint: Here, we use this below formula circumference,C=2\pi r

Given:Circumference circle with error is 0.01\; cm       


Circumference,C=2\pi r

\begin{aligned} &r=\frac{14}{\pi} \text { as } \mathrm{C}=28 \mathrm{~cm} \\\\ &\text { Also } \quad \frac{d C}{d r}=2 \pi \end{aligned}

Area circle,

        A=\pi r^{2}

\begin{aligned} &\text { So, } &A=\frac{(14)^{2}}{\pi} \end{aligned}

\text { Also } \quad \frac{d A}{d r}=2 \pi r

                \frac{d A}{d C}=\frac{\frac{d A}{d r}}{\frac{d C}{d r}}=r=\frac{14}{\pi}

Approximate error in A is

            \begin{aligned} d A &=\frac{d A}{d C} \times \Delta C \\\\ &=\frac{14}{\pi} \times \frac{1}{100} \\\\ &=\frac{1}{1400} \text { of } A \end{aligned}

So, percentage of error in   A=\frac{1}{14} \%

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