A) 7 sq. cm/min
B) 10 sq. cm/min
C) 17.5 sq. cm/min
D) 28 sq. cm/min
Correct Answer: B
Solution :
Volume =\[V=\frac{4}{3}\pi {{r}^{3}}\]Þ \[\frac{dV}{dt}=4\pi {{r}^{2}}.\frac{dr}{dt}\], at \[r=7\] cm 35 cc/min =\[4\pi {{(7)}^{2}}\frac{dr}{dt}\Rightarrow \frac{dr}{dt}=\frac{5}{28\pi }\] Surface area, S = \[4\pi {{r}^{2}}\] \[\frac{dS}{dt}=8\pi r\frac{dr}{dt}=\frac{8\pi .7.5}{28\pi }=10\,\]cm2/min.
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