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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?

  1. A \( 8 \pi \mathrm{cm}^{2} s^{-1} \)
  2. B \( 80 \pi \mathrm{cm}^{2} s^{-1} \)
  3. C \( 6 \pi \mathrm{cm}^{2} s^{-1} \)
  4. D \( 0 \frac{8}{3} \mathrm{~cm}^{2} s^{-1} \)
Verified Solution

Answer & Solution

Correct Answer

(B) \( 80 \pi \mathrm{cm}^{2} s^{-1} \)

Step-by-step Solution

Detailed explanation

\( A = \pi r^2 \) \( \frac{dA}{dt} = 2\pi r \frac{dr}{dt} \)