A) 1.5 sq cm/s
B) 0.5 sq cm/s
C) 5 sq cm/s
D) 3 sq cm/s
E) 0.04 sq cm/s
Correct Answer: A
Solution :
Circumference of circle \[C=2\pi r\] \[\Rightarrow \] \[\frac{dC}{dt}=2\pi \frac{dr}{dt}\] \[\Rightarrow \] \[\frac{0.3}{2\pi }=\frac{dr}{dt}\] \[\left( \because \frac{dC}{dt}=0.3\,cm/s\,given \right)\] Now, \[A=\pi {{r}^{2}}\] \[\frac{dA}{dt}=2\pi r\frac{dr}{dt}\] \[\Rightarrow \] \[\frac{dA}{dt}=r\times 0.3\] \[\Rightarrow \] \[{{\left[ \frac{dA}{dt} \right]}_{r=5}}=5\times 0.3=1.5\,sq\,cm/s\]
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