A) \[4\pi \]
B) \[2\pi \]
C) \[6\pi \]
D) \[3\pi \]
Correct Answer: A
Solution :
[a] Let A sq. units in the area measure when the radius is r units. Their \[A=\pi {{r}^{2}}\] Differentiate both side \[w.r.t't'\frac{dA}{dt}=2\pi r\frac{dr}{dt}\] ? (i) We have, \[\frac{dA}{dt}=3c\frac{dr}{dt}\] From eqn. (i), we get \[3c.\frac{dr}{dt}=2\pi r.\frac{dr}{dt}\] \[\Rightarrow 3c=2\pi r\] Now, \[c=\frac{2}{3}\pi (6)=4\pi \] when \[r=6\]
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