00:01
All right, so we got a classic related rates problem here.
00:04
So we have this oil spill in a circular pattern.
00:08
And so we have this radius that is increasing as the oil is spilling more and more and more.
00:15
So we're told that the radius is increasing at a rate.
00:18
So it's not that r is one.
00:21
It's that the rate of the radius is increasing per unit.
00:26
So we call this drdt.
00:28
So the rate at which the radius is increasing per unit of time is one meter per second.
00:34
So that's something we know.
00:35
And we're looking for.
00:37
It says how fast is the area of the spill increasing? so that's what's the rate of change of the area? so we're going to say d .a over dt is what i want to know.
00:48
Now, i notice the rate is increasing.
00:51
So that means the drdt is positive.
00:53
If it was shrinking and a different type of problem, that would be negative.
00:56
So now i need an equation that really.
00:58
Relates area and radius, well, that is just our area of a circle problem or our equation.
01:04
So we have the area of a circle is pi r squared.
01:07
Now that's fine.
01:08
We could plug in 37 and figure out the area at this moment, but we don't want to know what the area is.
01:13
We want to know the rate...