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## Sectors

# Area of a sector

CCSS.Math:

## Video transcript

A circle with area
81 pi has a sector with a 350-degree central angle. So this whole sector right
over here that's shaded in, this pale orange-yellowish
color, 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 like that. And they ask us, what is
the area of the sector? So we just need to realize
that 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. And 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 35/36. And so our area, our sector
area, is equal to-- let's see, in the numerator, we have
35 times-- instead of 81, let's see, that's going
to be 9 times 9 pi. And in 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. And neither of these
are divisible by 4, so that's about as
simplified as we can 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. Did 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.