Applications Of Derivatives Question 115
Question: If the rate of increase of area of a circle is not constant but the rate of increase of perimeter is constant, then the rate of increase of area varies
[SCRA 1996]
Options:
A) As the square of the perimeter
B) Inversely as the perimeter
C) As the radius
D) Inversely as the radius
Show Answer
Answer:
Correct Answer: C
Solution:
Perimeter $ P=2\pi r $
$ \frac{dP}{dt}=2\pi .,\frac{dr}{dt} $ and $ A=\pi r^{2} $
$ \frac{dA}{dt}=2\pi r.\frac{dr}{dt} $
therefore $ \frac{dA}{dt}=\frac{dP}{dt}\times r $
therefore $ \frac{dA}{dt}\propto r $ .
BETA
