A) \[\frac{1}{15\pi }ft/\min \]
B) \[\frac{1}{30\pi }ft/\min \]
C) \[\frac{1}{20}ft/\min \]
D) \[\frac{1}{25}ft/\min \]
E) None of these
Correct Answer: B
Solution :
Given,\[\frac{dV}{dt}=30f{{t}^{3}}/\min \]and\[r=15\text{ }ft\] Volume of spherical balloon \[V=\frac{4}{3}\pi {{r}^{3}}\] \[\Rightarrow \] \[\frac{dV}{dt}=4\pi {{r}^{2}}\frac{dr}{dt}\] \[\Rightarrow \] \[30=4\pi {{r}^{2}}\frac{dr}{dt}\] \[\Rightarrow \] \[\frac{dr}{dt}=\frac{30}{4\times \pi \times 15\times 15}\] \[=\frac{1}{30\pi }ft/\min \]
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