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Please solve RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 13 maths textbook solution

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Answer:  2.16 \pi m^{2}

Hint: Here, we use the surface area of the sphere (s)

s=4 \pi r^{2}

Given: r=9 \mathrm{~m} \text { and } \Delta r=0.03 \mathrm{~m}

Solution:  s=4 \pi r^{2}

\begin{aligned} &\frac{d s}{d x}=8 \pi r \\\\ &d s=\left(\frac{d s}{d x}\right) \Delta r \\\\ &=(8 \pi r) \Delta r \end{aligned}

\begin{aligned} &=8 \pi(9)(0.03) m^{2} \\\\ &=2.16 \pi m^{2} \end{aligned}

  Hence, the approximate error in circulating the surface area is 2.16 \pi m^{2}

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