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explain solution rd sharma class 12 chapter 12 derivatives as a rate measure exercise fill in the blanks question 12 maths

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Answer:\frac{dA}{dt}=12\pi \; cm^{2}/sec

Hint: Here we use the formula of area of circle (A) with radius r is given by

Given:A=\pi r^{2}

Solution:    \frac{dA}{dt}=\frac{d\left ( \pi r^{2} \right )}{dt}\times \frac{dr}{dt}=2\pi r\frac{dr}{dt}                     .......[by chain rule]

It is given that

                    \frac{dr}{dt}=3\; cm/s

               \therefore \frac{dA}{dt}=2\pi r(3)=6\pi r

Thus, when r=2 cm

               \therefore \frac{dA}{dt}=6\pi(2)=12\pi \; cm^{2}/s

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