A) As the square of the perimeter
B) Inversely as the perimeter
C) As the radius
D) Inversely as the radius
Correct Answer: C
Solution :
Perimeter \[P=2\pi r\] \[\frac{dP}{dt}=2\pi .\,\frac{dr}{dt}\]and \[A=\pi {{r}^{2}}\] \[\frac{dA}{dt}=2\pi r.\,\,\frac{dr}{dt}\] Þ \[\frac{dA}{dt}=\frac{dP}{dt}\times r\]Þ \[\frac{dA}{dt}\propto r\].
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