00:01
So for this problem, we can go ahead and start out by making a diagram of our situation.
00:05
So we know that we have a clock and our minute hand is going to be six inches long.
00:10
And we're starting at 12 o 'clock.
00:13
So we know that our minute hand is initially going to start out like this.
00:16
And again, we know that our hand is six inches long.
00:20
And we want to know how fast the area is increasing in inches squared per minute.
00:24
So essentially, we know that our area is going to be this area.
00:30
Say for instance if our time was about 1215 here then that means that we are going to be able to use our formula for area of a sector of a circle and that formula is that our area is equal to one -half times r squared times the angle um so theta so theta is this angle right here theta and what we're solving for is how fast the area is increasing so that means that we're solving for d a d t and we're going to be able to find the rate of change d theta d t using the fact that this is a clock.
01:06
So essentially we know that our minute hand is going to go around the clock entirely one time, which is two pi radians in one hour, so per 60 minutes...