sector abc sits inside a circle with a radius of 9cm and is a 80 degree angle what is the area of sector abc

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

3279.82 cubic inches

53746.66 cm³

53.75 liters

Step-by-step explanation:

I hope this helps u! :D