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  • Need solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 3

Need solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 3

Answers (1)

Answer: 3k%

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

                V=\frac{4}{3} \pi r^{3}

Given:  Percentage error in measuring radius=k%

Solution:

Here, volume of sphere is

V=\frac{4}{3} \pi r^{3}

Let’s differentiate,

\frac{d V}{d r}=4 \pi r^{2}

Given percentage error in measuring radius=k%

So,

\begin{aligned} &\frac{\Delta r}{r}=\frac{k}{100} \\\\ &\Delta r=\frac{r k}{100} \end{aligned}

Now, approximate error in measuring

\begin{aligned} V &=d V=\left(\frac{d V}{d r}\right) \Delta r \\\\ &=\frac{k}{100} 4 \pi r^{3} \\\\ &=\frac{3 k}{100} V \\\\ &=3 k \% \text { of } V \end{aligned}

So, percentage error in measuring V=3 k \%

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