Test 4 Section 3 - #19 (page 586)

Because we're looking at only 30 degrees, we can figure out what fraction of the circle this slice is. The whole circle would have 360 degrees, so this is only 30/360, or 1/12 of the whole circle. Now use the rest of the info we're given: we know the length of the arc is 6π, and since this is 1/12 of the whole circle, 6π must be 1/12 of the whole circumference. Multiplying 6π times 12 gives us 72π, which would be the circumference of the whole circle. Since circumference = (π)(diameter), the diameter must be 72, and the radius would then be 36.

Still with me? Next step is to find the area of the whole circle. Since the radius is 36, the area would be (36²)(π), which is 1296π. But that's the area of the WHOLE circle; we're only looking at a slice that's 1/12 of the whole circle. So the slice would have an area of 1/12 of 1296π, which is 108π.