A) \[\frac{9}{7}\]
B) \[\frac{7}{9}\]
C) \[\frac{2}{9}\]
D) \[\frac{9}{2}\]
Correct Answer: C
Solution :
\[V=\frac{4}{3}\pi {{r}^{3}}\] \[4500\pi =\frac{4\pi {{r}^{3}}}{3}\] \[\frac{dV}{dt}=4\pi {{r}^{2}}\left( \frac{dr}{dt} \right)\] \[45\times 45\times 3={{r}^{3}}\] \[r=15\,\,m\] after \[49\,\min =(4500-49.72)\pi =972\,\pi \,{{m}^{3}}\] \[972\pi =\frac{4}{3}\pi {{r}^{3}}\] \[{{r}^{3}}=3\times 243=3\times {{3}^{5}}\] \[r=9\] \[72\pi =4\pi \times 9\times 9\left( \frac{dr}{dt} \right)\] \[\frac{dr}{dt}=\left( \frac{2}{9} \right)\]
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