00:01
All right, so we are given a circle with a radius of r equals 9, and then we're trying to find arc length and area of a sector given different angles.
00:10
The first two angles a and b are in radians, and you can tell that because of that pi, 9 pi over 7, that means it's in radians.
00:19
So in radians, we have equations for arc length and area of a sector.
00:28
The length is just pi, is the angle theta times r, the radius, and then the area is theta, the angle, times r squared divided by 2.
00:41
So this is what we're going to use for a and b, these two.
00:45
A is the arc length, so we're using that l formula.
00:48
The angle is 9 pi over 7, and then the radius is 9.
00:54
That's like the same thing as 9 over 1.
00:56
So we just multiply across, 81 pi over 7, and that's your first answer.
01:02
For b, we're doing area of a sector, so we're going to do that area, and it's going to be the same idea, 9 pi over 7 for the theta times 9 squared, r squared, divided by 2.
01:19
So on the top, we have 9 pi over 7 times 81, if we do 9 squared over 1.
01:26
So multiplying across, 9 times 9, uh, times 9 gives us 729 pi over 7, and then we're still dividing by 2, so that just means that we're doing 729 pi over 7 times 1 half.
01:44
Dividing by 2 and multiplying by 1 half are the same thing, so this is 729 pi over 14, and that's your area of the sector...