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

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

Answers (1)

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       

Solution:

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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