Applications Of Derivatives Question 173
Question: Gas is being pumped into a spherical balloon at the rate of 30 ft3/min. Then the rate at which the radius increases when it reaches the value 15 ft is
[EAMCET 2003]
Options:
A) $ \frac{1}{30\pi }ft/\min \text{.} $
B) $ \frac{1}{15\pi }ft/\min \text{.} $
C) $ \frac{1}{20}ft/\min \text{.} $
D) $ \frac{1}{25}ft/\min \text{.} $
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Answer:
Correct Answer: A
Solution:
Given that $ dV/dt=30ft^{3}/min $ and $ r=15ft $
$ V=\frac{4}{3}\pi r^{3}; $
$ \frac{dV}{dt}=4\pi r^{2}\frac{dr}{dt} $
$ \frac{dr}{dt}=\frac{dV/dt}{4\pi r^{2}}=\frac{30}{4\times \pi \times 15\times 15}=\frac{1}{30\pi } $ ft/min
BETA
