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need solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 3

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Answer: 2 k \pi c m^{2}

Hint: Here, Area of a circular plate of radius  x is given by A=\pi x^{2}

Given: the radius of a circular plate initially is 10 cm and it increase by K%

Solution: Suppose x be the radius of the plate, and \Delta x is the change in the value of x

Thus we have x=10 \text { and } \Delta x=\frac{K}{100} \times 10

So,  \Delta x=0.1 K

Differentiating A with respect to x

\begin{aligned} &\frac{d A}{d x}=\frac{d}{d x}\left(\pi x^{2}\right) \\\\ &\frac{d A}{d x}=\pi \frac{d}{d x}\left(x^{2}\right)=n x^{n-1} \\\\ &\Rightarrow \frac{d A}{d x}=2 \pi x \end{aligned}

\begin{aligned} &\Rightarrow \text { when } x=10 \text { and } \frac{d A}{d x}=2 \pi(10) \text { so, } \frac{d A}{d x}=20 \pi \\\\ &\Rightarrow \Delta y=\frac{d y}{d x} \Delta x \end{aligned}

\begin{aligned} &\text { Here, } \frac{d A}{d x}=20 \pi \text { and } \Delta x=0.1 K \\\\ &\Delta A=(20 \pi)(0.1 K) \\\\ &\Delta A=2 K \pi \end{aligned}

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