A) \[\frac{1}{{{r}^{2}}}\]
B) \[\frac{1}{r}\]
C) \[{{r}^{2}}\]
D) \[r\]
Correct Answer: C
Solution :
Here we have \[\frac{dr}{dt}=2\,cm/\sec \] and surface area of sphere is given by \[A=\frac{4}{3}\pi {{r}^{3}}\] \[\therefore \] \[\frac{dA}{dt}=3\times \frac{4}{3}\pi {{r}^{2}}\frac{dr}{dt}\] \[=4\pi {{r}^{2}}(2)\] \[=8\pi {{r}^{2}}\] \[\therefore \] \[\frac{dA}{dt}\propto {{r}^{2}}\]You need to login to perform this action.
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