Applications Of Derivatives Question 6
Question: The radius of a circle is uniformly increasing at the rate of 3 cm/s. What is the rate of increase in area, when the radius is 10 cm ?
Options:
A) $ 6\pi cm^{2}/s $
B) $ 10\pi cm^{2}/s $
C) $ 30\pi cm^{2}/s $
D) $ 60 \pi cm^{2}/s $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Given $ \frac{dr}{dt}=3 $ Let $ \text{A=Area}ofcircle=\pi r^{2}. $
$ \therefore \frac{dA}{dt}=2\pi r.\frac{dr}{dt}=6\pi r $ Now, $ {{. \frac{dA}{dt} |}_{r=10}}=6\times 10\times \pi =60\pi cm^{2}/s $
BETA
