Applications Of Derivatives Question 178
Question: A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of 50 cm3/min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is
[AIEEE 2005]
Options:
A) $ \frac{1}{54\pi } $ cm/min
B) $ \frac{5}{6\pi } $ cm/min
C) $ \frac{1}{36\pi } $ cm/min
D) $ \frac{1}{18\pi } $ cm/min
Show Answer
Answer:
Correct Answer: D
Solution:
$ V=\frac{4}{3}\pi ,{{x}^{3}} $ where x is thickness of ice. $ \therefore $ $ \frac{dV}{dt}=4\pi {{(10+x)}^{2}}\frac{dx}{dt} $
$ =a^{x}b^{2x-1}(\log ab^{2})^{2} $ At $ x=5 $ , $ ( \frac{dx}{dt} )=\frac{1}{18\pi }cm/\min . $
BETA
