Question

A rock is tossed into a pond creating an expanding circular ripple. If the radius of the ripple is increasing at a rate of 1.5 ft/sec, find out how fast the area is increasing when the radius is 2 feet.

Answer 1

help

Answer 2

dr/dt=1.5

Since

A=pi*r^2/4

differentiate both sides to give rate of area increase.

dA/dt=pi/4*2r*(dr/dt)

plug in values for dr/dt and r

Answer 3

Is it not the case that A=Pi * r^2 ?