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Explain solution RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 4 maths

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Answer: \text { (c) } 3 \alpha \%


Hint: Here, we all know the formula of volume of cylinder

            V=\pi r^{2} h


Percentage error in measuring height=3 \alpha \%


Here, volume of cylinder, V=\pi r^{2} h

But here , h=r

So,     \begin{aligned} &V=\pi r^{2} \times r \\\\ & \end{aligned}

          V=\pi r^{3}

Let’s differentiate

        \frac{d V}{d h}=3 \pi h^{2}

Given percentage error in measuring height=3 \alpha \%

So,        \Delta h=\frac{\alpha h}{100}

Now, approximate error in measuring

\begin{gathered} V=d V=\left(\frac{d V}{d h}\right) \Delta h \\\\ =\frac{3 \alpha}{100} \pi h^{3} \\\\ =3 \alpha \% \text { of } V \end{gathered}

So, percentage error in measuring, 3 \alpha \%

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