JEE Exam  >  JEE Questions  >  A stone is dropped into a quiet lake and wave... Start Learning for Free
A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​
  • a)
    Decreasing at the rate of 48π cm2 / sec
  • b)
    Increasing at the rate of 24π cm2 / sec
  • c)
    Increasing at the rate of 48π cm2 / sec
  • d)
    Decreasing at the rate of 24π cm2 / sec
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A stone is dropped into a quiet lake and waves move in circles at a sp...
Rate of increase of radius dr/dt = 2 cm/s
Area of circle A = πr2
dA/dt = π*(2r)*(dr/dt)
= π*(24)*2
= 48π cm2/s
Rate of increase of area is 48π cm2/s (increasing as it is positive).
Free Test
Community Answer
A stone is dropped into a quiet lake and waves move in circles at a sp...
Given: Speed of waves = 2 cm/s, Radius of wave = 12 cm

We need to find the rate of change of the enclosed area at that instant.

Formula: Area of circle = πr^2

Differentiating with respect to time, we get:

dA/dt = 2πr (dr/dt)

Here, r = 12 cm and dr/dt = 2 cm/s

dA/dt = 2π(12)(2) = 48π cm^2/s

dA/dt = 48π cm^2/s ≈ 150.8 cm^2/s (taking π ≈ 3.14)

Therefore, the enclosed area is increasing at the rate of 48 cm^2/s (Option C).
Explore Courses for JEE exam
A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer?
Question Description
A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A stone is dropped into a quiet lake and waves move in circles at a speed of 2cm per second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area changing ?​a)Decreasing at the rate of 48π cm2/ secb)Increasing at the rate of 24π cm2/ secc)Increasing at the rate of 48π cm2/ secd)Decreasing at the rate of 24π cm2/ secCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev