i hope this will help you to solve your problem here is a link under if you what it more detail
tutor for this video we want to work on
00:04
finding the area of a sector of a circle
00:06
so the idea behind that is here we have
00:08
a circle and if I mark out a certain
00:11
angle I have just a portion of the
00:13
circle that's what we call it sector and
00:14
I'm curious well what is the area of
00:16
that sector now there's a really neat
00:18
formula that you can use that relates
00:20
the radius and the angle to the area of
00:23
that portion and looks something like
00:25
this it says that the area equals 1/2
00:27
multiplied by the radius squared
00:29
multiplied by the angle as long as that
00:32
angle is written in radians so it's
00:35
really neat and handy formula that you
00:36
can quickly figure out the area of
00:38
something like that
00:39
we'll do a couple of examples so you can
00:41
see how this formula works but also see
00:44
how even if you don't have exactly the
00:46
radius and angle sometimes you can still
00:48
find it if you have just enough
00:49
information so the first one we're going
00:53
to do is this circle right here it has a
00:55
radius of 10 and it's marking out an
00:58
angle of 3 PI over 4 so we're really
01:00
curious about the area of just this
01:03
region up here so we're going to borrow
01:05
our formula area equals 1/2 times the
01:09
radius squared times the angle and start
01:12
dropping in our information so for this
01:16
one our radius is going to be 10 that
01:18
gets squared and our angle is already in
01:21
radians so we'll go ahead and just leave
01:23
it as 3 pi divided by 4 and now we work
01:26
to simplify this let's see what we get
01:28
so 10 squared is 100 I'll be divided by
01:32
2 and we still have our 3 pi divided by
01:35
4 so now we're reducing this 4 goes into
01:39
120 5 times
01:43
let's see nothing else can really cancel
01:45
so 25 times 3 is 75 pi all divided by 2
01:50
so that is the area now be careful when
01:54
you're doing problems like this
01:55
sometimes people see this and they
01:57
almost automatically think they still
01:59
have an angle I think because there's a
02:00
PI in it
02:02
this really is an area it's just written
02:04
in terms of pi if you want a decimal you
02:07
can go ahead and punch this in a
02:08
calculator and then get the decimal
02:09
equivalent for that area all right let's
02:12
do one more example
02:14
and see how this one turns out so for
02:17
this one I have a circle has a radius of
02:19
4 but I don't really know what the angle
02:22
is on the inside what I do know is it
02:24
has this little arc out here and the arc
02:26
is 3 pi so immediate if try and jump in
02:31
that formula I'm missing some
02:32
information I'm missing this fact that
02:33
you know I don't have that little angle
02:35
that's ok because the interior angle
02:38
this arc and radius are related with
02:41
another formula arc length equals radius
02:44
times theta so we can use this to get
02:46
our foot in the door and actually figure
02:47
out what this angle is and then jump
02:50
into our area formula all right so let's
02:52
give this a try so my arc length is 3 pi
02:55
my radius is 4 but what I don't know is
02:58
my angle no problem divide both sides by
03:01
4 that'll give us our angle and now we
03:07
can move forward with this and actually
03:09
figure out the area so area equals 1/2
03:12
radius squared times angle where my
03:17
radius is still the 4 so 4 squared but
03:21
now I know my angle it's 3 PI over 4 and
03:24
now we work to simplify this so 4
03:28
squared is 16 now B divided by 2 3 PI
03:32
divided by 4 let's go ahead and cancel
03:35
out some extra terms in here let's see 4
03:38
goes into 16 4 times then 2 goes into 4
03:41
twice and so it looks like the only
03:44
thing we have left is just the 2 times
03:45
the 3 or 6 pi so again that represents
03:50
the area of this portion of the circle
03:53
right up there not too bad so if you
03:56
haven't already done so maybe start
03:57
memorizing that formula it is kind of
03:59
handy when making those connections and
04:01
A= r^2 .4/2
