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  • Explain solution RD Sharma class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 4 maths

Explain solution RD Sharma class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 4 maths

Answers (1)

Answer:

0.002 \mathrm{~cm} / \mathrm{sec} \quad (D)

Hint:

V(r, h)=\frac{1}{3} \pi r^{2} h

Given:

h=2 r \text { and } \frac{d V}{d t}=40 \mathrm{~cm}^{3} / \mathrm{sec}

Solution:

\begin{aligned} &V(r)=\frac{2}{3} \pi r^{3}\\ &\rightarrow \text { Differentiating (i) with respect to } t\\ &\frac{d V}{d t}=2 \pi r^{2} \frac{d r}{d t}\\ &40=2 \pi \times 10000 \times \frac{d r}{d t}\\ &\frac{d r}{d t}=0.002 \mathrm{~cm} / \mathrm{sec} \end{aligned}

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Gurleen Kaur

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