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need solution for rd sharma maths class 12 chapter 12 derivatives as a rate measure exercise fill in the blanks question 7

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Answer: \frac{1}{30\pi }ft/min

Hint: Here we use the formula of volume, V=\frac{4}{3}\pi r^{3}

Given:\frac{dV}{dt}=30\; cm^{3}/sec

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

              \frac{dV}{dt}=4\pi r^{2}\left ( \frac{dr}{dt} \right )

               \frac{dr}{dt}= \left [ \frac{dV}{dt} \right ]/4\pi r^{2}

               \frac{dr}{dt}= \left [ \frac{30}{\left [ 4\times \pi \times 15\times 15 \right ]} \right ]

                    = \frac{1}{30\pi }ft/min   

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