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  • Please solve RD Sharma class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 5 maths textbook solution

Please solve RD Sharma class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 5 maths textbook solution

Answers (1)

Answer:

1m/minute

Hint:

The volume of a cylinder, with radius r and height h is defined by

Given:

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

Solution:

Substituting\; r=0.5\; \mathrm{~m} \\ we\; get \\ Given\; that\; \frac{d V}{d t}=0.25 \pi \mathrm{m}^{3} / \mathrm{min}, \;we \;have \;to \;calculate \;\frac{d h}{d t} \\ \rightarrow Di\! f\! \! f\! erentiating \;(i)\; with\; respect\; to\; t

\begin{aligned} &\frac{d V}{d t}=\pi r^{2} \frac{d h}{d t} \\ &\frac{d h}{d t}=\frac{1}{\pi r^{2}} \times \frac{d V}{d t} \\ &\frac{d h}{d t}=\frac{0.25 \pi}{\pi(0.5)^{2}} \\ &\frac{d h}{d t}=\frac{0.25 \pi}{0.25 \pi} \\ &\frac{d h}{d t}=1 \mathrm{~m} / \mathrm{min} \end{aligned}

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Gurleen Kaur

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