Question

A stone is dropped onto a lake, creating a circular ripple that travels outward at a speed
of 50in=sec. Find the rate at which the area within the circular ripple is increasing after
1sec and 3sec

Answer 1

So this is a typical related rates problem with an increasing circle..

Answer 2

First write the formula for the Area of the circle:
A = pi*r^2

Answer 3

dA/dt is the rate at which the circle is increasing, which is also the derivative:
dA/dt = 2*pi*r*(dr/dt)

Answer 4

hmm actually what do they mean by is traveling outward? Does that mean the radius is increasing?

Answer 5

correct i believe that is exactly how it is written, I was hoping someone might know what they meant.

Answer 6

Oh i think it is the radius.. let us just work it out and see for ourselves..

Answer 7

So:
dA/dt = 2*pi*r*(dr/dt)
the radius is increasing at the rate of 50 in/sec
So in one second, the radius increased from 0 to 50in. So:
dA/dt = 2*pi*50*50 = = 5000pi

Answer 8

In 3 seconds radius increased from 0 to 150in. So:
dA/dt = 2*pi*150*50 = = 15000 pi check the answers..

Answer 9

ok that s what I was thinking but I didnt want to be wrong when I have a test in 45 min. thank you very much.