Area of a sector

a circle with area 81 pi has a sector with a 350-degree central angle so this whole sector right over here that shaded in this kind of pale orange LOH color that has a that has a 350-degree central angle so you see the central angle it's a very large angle it's going all the way around all the way around like that and they asked us what is the area of the sector so we just need to realize the ratio between the area of the sector area of sector the area the ratio between the area of the sector and the total area of the circle and they tell us what the total area is it's 81 pi + 81 pi is going to be equal to the ratio of its central angle which is 350 degrees over the total number of degrees in a circle over 360 so the area of the sector over the total area is equal to the degrees in the central angle over the total degrees in a circle and then we just can solve for area of a sector by multiplying both sides by 81 pi 81 pi 81 pi so these cancel out 350 divided by 360 is 35 over 36 and so our area our sector area sector area is equal to C in the numerator we have 35 times instead of 81 I'm just going to write that as let's see that's going to be 9 times 9 PI and the denominator I have 36 well that's the same thing as 9 times 4 and so we can divide the numerator and the denominator both by 9 and so we are left with 35 times 9 35 times 9 and neither of these are divisible by 4 so that's about as simplified as we could get it so let's think about what 35 times 9 is 35 times 9 it's going to be 350 minus 35 which would be 315 I guess 350 Dean should I do that right yeah it's going to be 270 plus 45 which is 315 PI over 4 315 PI over 4 is the area of the sector