KCET · Maths · Functions
A stone is dropped into a quiet lake and waves move in circles at the speed of \( 5 \mathrm{cms}^{-1} \). At that
instant, when the radius of circular wave is \( 8 \mathrm{~cm} \), how fast is the enclosed area increasing?
- A \( 8 \pi \mathrm{cm}^{2} s^{-1} \)
- B \( 80 \pi \mathrm{cm}^{2} s^{-1} \)
- C \( 6 \pi \mathrm{cm}^{2} s^{-1} \)
- D \( 0 \frac{8}{3} \mathrm{~cm}^{2} s^{-1} \)
Answer & Solution
Correct Answer
(B) \( 80 \pi \mathrm{cm}^{2} s^{-1} \)
Step-by-step Solution
Detailed explanation
\( A = \pi r^2 \) \( \frac{dA}{dt} = 2\pi r \frac{dr}{dt} \)
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