Answer to Question #268655 in Calculus for Jess

Question

A stone is dropped into a pool of water. The radius of the circular ripple formed increases at 4 𝑚/𝑠. Calculate the rate at which the area of the ripple is increasing when the radius is 6m.

Answer 1

$\frac{dr}{dt}=4m/s$

$A=πr²=>\frac{dA}{dr}=2πr$

$\frac{dA}{dt}=\frac{dA}{dr}•\frac{dr}{dt}$

$=>\frac{dA}{dt}=2πr•4=8πrm²/s$

when $r=6m$

$\frac{dA}{dt}=8π(6)=48πm²/s$