#### Provide solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise  multiple choice question 8

Answer: $\text { (c) } 3 \lambda \%$

Hint: Here, we all know the formula about volume of cone

$V=\frac{1}{3} \pi r^{2} h$

Given:

$\frac{r}{h}=\frac{1}{2}$

So, volume of cone  $V=\frac{1}{3} \pi r^{2} h$

Solution:

So,

\begin{aligned} &V=\frac{1}{3} \pi r^{2}(2 r) \\\\ &V=\frac{2}{3} \pi r^{3} \end{aligned}

Let’s differentiate,

\begin{aligned} &V=\frac{2}{3} \pi r^{3} \\\\ &\frac{d V}{d r}=2 \pi r^{2} \end{aligned}

Percentage error in measuring$=\lambda \%$

\begin{aligned} &\frac{\Delta r}{r}=\frac{\lambda}{100} \\\\ &\Delta r=\lambda r(100) \end{aligned}

Approximate error in $V=dV$

\begin{aligned} &=\frac{d V}{d r} \times \Delta r \\\\ &=\frac{\lambda}{100}\left(2 \pi r^{3}\right) \end{aligned}

\begin{aligned} &=\frac{3 \lambda}{100}\left(\frac{2}{3} \pi r^{3}\right) \\\\ &=3 \lambda \% \text { of } V \end{aligned}

So, percentage error in $V=3\lambda \%$