Applications Of Derivatives Question 185
Question: The radius of a cylinder is increasing at the rate of 3 m/sec and its altitude is decreasing at the rate of 4m/sec. The rate of change of volume when radius is 4 meters and altitude is 6 meters is
[Kerala (Engg.) 2005]
Options:
A) $ 80\pi , $ cu. m/sec
B) $ 144,\pi , $ cu. m/sec
C) $ 80, $ cu. m/sec
D) $ 64, $ cu. m/sec
E) $ -80,\pi $ cu. m/sec
Show Answer
Answer:
Correct Answer: A
Solution:
$ V=\pi r^{2}h $ ; $ \frac{\partial V}{\partial t}=\pi [ 2r\frac{\partial r}{\partial t}h+r^{2}\frac{\partial h}{\partial t} ] $
$ \frac{\partial V}{\partial t}=\pi ,[2(4),(3),(6),+,{{(4)}^{2}}(-4)]=\pi ,[144-64]=80,\pi cu,m/sec $ .
BETA
