A) \[-\pi \,c{{m}^{2}}/s\]
B) \[10\pi \,c{{m}^{2}}/s\]
C) \[0.1\pi \,c{{m}^{2}}/s\]
D) \[5\pi \,c{{m}^{2}}/s\]
E) \[\pi \,c{{m}^{2}}/s\]
Correct Answer: E
Solution :
Given that,\[\frac{dr}{dt}=0.1\text{ }cm/s\] \[\therefore \]Area, \[A=\pi {{r}^{2}}\] On differentiating w.r.t. r, we get \[\Rightarrow \] \[\frac{dA}{dt}=2\pi r\frac{dr}{dt}\] \[\therefore \] \[{{\left. \frac{dA}{dt} \right|}_{r=5}}=10\pi \times 0.1=\pi c{{m}^{2}}/s\]
You need to login to perform this action.
You will be redirected in
3 sec
