A) 10
B) \[\sqrt{10}\]
C) \[100\]
D) \[10\sqrt{10}\]
Correct Answer: A
Solution :
Volume of sphere \[V=\frac{4}{3}\pi {{r}^{3}}\] \[\frac{dV}{dt}=\frac{4}{3}.\pi .3{{r}^{2}}.\frac{dr}{dt}\] \[35=4\pi {{r}^{2}}.\frac{dr}{dt}\]or\[\frac{dr}{dt}=\frac{35}{4\pi {{r}^{2}}}\] Surface area of sphere \[=S=4\pi {{r}^{2}}\] \[\frac{dS}{dt}=4\pi \times 2r\times \frac{dr}{dt}=8\pi r.\frac{dr}{dt}\] \[\frac{dS}{dt}=\frac{70}{r}\] (By using (1)) Now, diameter =14 cm, r = 7\[\therefore \]\[\frac{dS}{dt}=10\]
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