Applications Of Derivatives Question 89
Question: If a circular plate is heated uniformly, its area expands 3c times as fast as its radius, then the value of c when the radius is 6 units, is
Options:
A) $ 4\pi $
B) $ 2\pi $
C) $ 6\pi $
D) $ 3\pi $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Let A sq. units in the area measure when the radius is r units. Their $ A=\pi r^{2} $
Differentiate both side $ w.r.t’t’\frac{dA}{dt}=2\pi r\frac{dr}{dt} $ - (i) We have, $ \frac{dA}{dt}=3c\frac{dr}{dt} $
From eqn. (i), we get $ 3c.\frac{dr}{dt}=2\pi r.\frac{dr}{dt} $
$ \Rightarrow 3c=2\pi r $ Now, $ c=\frac{2}{3}\pi (6)=4\pi $ when $ r=6 $
BETA
