Question

A stone is dropped into a pond. Waves in the form of circles are generated and the radius of the outermost ripple increases at the rate of 2 inch/sec when radius is 5 inch. Find the rate of increasing area.

Answer 1

$\begin{array}{cc}A=\pi r^2& \\ Diff.w.r.t,& \\ \frac{dA}{dt}=2\pi r.\frac{dr}{dt}& \left[\frac{dr}{dt}=2\right]\\ \frac{dA}{dt}=2\pi \times 5\times 2& \\ =20\pi inc{h}^2/\sec & \end{array}$