00:01
So we have our circle c and the two inner circles.
00:06
So i just pick these distances for the inner radius, and we want to find this area between the three circles.
00:14
So that area is going to be one half, the area of that big circle a, b.
00:24
So i'm going to call this circle little a, little b, little c.
00:30
So we want one half of the area of pi, c squared.
00:38
Minus pi a squared minus pi b squared.
00:44
The reason why we want half, so we're taking this big circle and subtracting the area of the little circle and the other circle.
00:51
We only want half because we only want one side of what's left.
00:56
So we can pull out that pi, and we get pi half, c squared minus a squared minus b squared.
01:06
So now we can plug in those radiuses.
01:08
So the area equals, so what is our radius c? so our diameter for c is 2 plus 2 plus 3 plus 3.
01:18
So it's going to equal 10.
01:20
So our radius is 5 minus the radius 4a, so 2 squared, and then the radius 4b3 squared.
01:29
So that's going to give us 25 minus 4 minus 9, which equals 12.
01:35
So that's going to give us an area of 6 pi.
01:43
It asks us to measure the arc lengths of the three semicircular arcs and note your observations.
01:50
So let's find the arc length of a, b, and c.
01:57
So the arc length is going to be circumference, which equals 2 pi r.
02:05
We only want half of each circumference.
02:07
So that's just going to equal pi r.
02:10
So let's, we know that b is pi r and c is pi r...