Applications Of Derivatives Question 169
Question: The rate of change of the surface area of a sphere of radius r when the radius is increasing at the rate of 2 cm/sec is proportional to
[Karnataka CET 2003]
Options:
A) $ \frac{1}{r} $
B) $ \frac{1}{r^{2}} $
C) $ \because $ Surface area $ s=4\pi r^{2} $ and $ \frac{dr}{dt}=2 $ \ $ \frac{ds}{dt}=4\pi \times 2r\frac{dr}{dt} $ = $ 8\pi r\times 2=16\pi r $
therefore $ \frac{ds}{dt}\propto r $ .
D) $ r^{2} $
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Answer:
Correct Answer: B
Solution:
$ r $
BETA
