Question

A single hailstone falls into a pool at the beginning of a thunderstorm. It makes a circular ripple. The radius increases at 2 cm/s, when the radius is 5cm. What is the rate of change of the area enclosed at this time?

Answer 1

\[\frac{1}{5\pi}\frac{cm}{s}\]

Answer 2

i.e. \[A=\pi r^2\]
\[\frac{dA}{dt}=2\pi r\frac{dr}{dt}\]
\[\frac{dr}{dt}=\frac{\frac{dA}{dt}}{2\pi (5)}\]

Answer 3

Thank you!!