Question-39 By dropping a stone in a quiet lake, a wave in the form of circle is generated. The radius of the circular wave increases at the rate of 2.1 cm/sec. Then the rate of increase of the enclosed circular region, when the radius of the circular wave is 10 cm, is (Given \pi=\frac{22}{7})
(A) 66\ cm^2/second
(B) 122\ cm^2/second
(C) 132\ cm^2/second
(D) 110\ cm^2/second
Answer: (C)
Explanation:
Given, the rate of increasing the radius
=\frac{dr}{dt} =2.1\ cm/sec.Area = A = \pi r^2
∴ \frac{dA}{dt}=2\pi r\frac{dr}{dt}
⇒ \frac{dA}{dt}=2\pi\times10\times2.1 …(∵ r=10\ cm)
=2\times\frac{22}{7}\times10\times2.1 =132\ cm^2/second