Applications Of Derivatives Question 8
Question: If by dropping a stone in a quiet lake a wave moves in circle at a speed of 3.5 cm/sec, then the rate of increase of the enclosed circular region when the radius of the circular wave is 10 cm, is $ ( \pi =\frac{22}{7} ) $
[MP PET 1998]
Options:
A) 220 sq. cm/sec
B) 110 sq. cm/sec
C) 35 sq. cm/sec
D) 350 sq. cm/sec
Show Answer
Answer:
Correct Answer: A
Solution:
Given the rate of increasing the radius $ =\frac{dr}{dt}=3.5cm/sec $ and $ r=10cm $ Area of circle $ =\pi r^{2} $ , $ A=\pi r^{2} $
therefore $ \frac{dA}{dt}=2\pi r.\frac{dr}{dt} $
therefore $ \frac{dA}{dt}=2\pi \times 10\times 3.5 $
therefore $ \frac{dA}{dt}=220cm^{2}/sec $ .
BETA
