A) \[70\,\pi \,\,c{{m}^{2}}/s\]
B) \[70\,\,c{{m}^{2}}/s\]
C) \[80\,\,\pi \,\,c{{m}^{2}}/s\]
D) \[80\,\,c{{m}^{2}}/s\]
Correct Answer: C
Solution :
Given,\[\frac{dr}{dt}=2\,\,cm/s,\] where \[r\] be radius of circle and \[t\] be the time. Now, area of circle is given by\[A=\pi {{r}^{2}}\] On differentiating w.r.t.\[r,\] we get \[\frac{dA}{dt}=2\pi \frac{dr}{dt}\] \[\Rightarrow \] \[\frac{dA}{dt}=2\pi \cdot 20\cdot 2\] \[\Rightarrow \] \[\frac{dA}{dt}=80\,\,\pi \,\,c{{m}^{2}}/s\] Thus, the rate of change of area of circle with respect to time is\[80\,\,\pi \,\,c{{m}^{2}}/s\].
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