Applications Of Derivatives Question 372
Question: Radius of a circle is increasing uniformly at the rate of $ 3cm/\sec . $ The rate of increasing of area when radius is $ 10cm $ , will be
Options:
A) $ \pi ,cm^{2}/s $
B) $ 2\pi ,cm^{2}/s $
C) $ 10\pi ,cm^{2}/s $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{dr}{dt}=3 $ , we have $ S=\pi r^{2}\Rightarrow \frac{dS}{dt}=2\pi r\frac{dr}{dt} $
therefore $ {{( \frac{dS}{dt} )} _{r=10}}=2.\pi \times 10\times 2=40,\pi ,cm^{2}/sec. $
BETA
