Is Arc AB 90 degrees?

- anonymous

Is Arc AB 90 degrees?

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

##### 1 Attachment

- anonymous

|dw:1378320193232:dw|

- anonymous

since the diameter of the circle is 4cm the radius = 2cm

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

yes but how will that help me find the arc AB

- anonymous

?

- anonymous

what is the circumference of the circle?

- amistre64

you dont need circumference to find area ....

- anonymous

|dw:1378320396866:dw|

- anonymous

let arc AB=x
then circumference/4= x

- anonymous

did you see what i did there?

- amistre64

the picture is asking to find the area of the shaded portion; even tho the post alludes to some arc length ...

- anonymous

the circumference of the circle is 2*pie*r = 2*3.14*2 = 12.56
arc AB = 12.56/4 = 3.14

- anonymous

yes i know but in order to find the area of the shaded sector i need to know the arc length first

- amistre64

you do not need to know the arc length in order to define the area ...

- amistre64

the central angle is 90 degrees (use radians for the area calcuation), that and the radius are all thats needed for the area

- anonymous

(arc lenth *pie*r)/360 = area

- anonymous

Arc of sector ACB = measurement of arc AB/360 degrees X pi X r^@

- amistre64

the measure of the angle is needed, not the length of the arc

- amistre64

\[\Large Area=\frac{\theta}{360}\pi r^2\]

- anonymous

@amistre64 there may be multiple ways to solve a problem

- amistre64

there may be :) but ive never quite seen using arclength to define area, can you proof it? or point to some literature for it?

- amistre64

it just seems like more effort than what its worth at the moment

- anonymous

##### 1 Attachment

- anonymous

yes ofcourse
arc length = theta*r (theta in radians)
substituting theta*r in your equation
we get area = (arc length*pie*r)/360

- amistre64

fair enough :)

- anonymous

yes..its given in d fig.

- anonymous

@hello1213 did you get the answer

- anonymous

no because i dont know the arc length

- anonymous

in the fig. its shown its right angled so its 90degree...

- anonymous

arch length is 3.14
if you want to know how we got that, scroll up and read again

- anonymous

Area of sector JLK = measurement of arc JK/360 degrees X pi X r^2
A=arc JK/360 X pi X 4

- anonymous

A= arc jk/360 X 12.566

- anonymous

the circle has 360degrees
so if the angle of the sector is 90 degrees
four such sectors can be made in the circle
each sector has equal arc lengths
so the circumference / 4 will give you the arch length

- anonymous

does that make sense

- anonymous

yes... what is the area of the shaded sector... its not making sense im getting about 0.11

- anonymous

area of the shaded region would be (arc length *pie*r)
you dont have to divide it by 360 i made a mistake

- anonymous

ok hold on

- anonymous

about 19.7 in.^2

- anonymous

yeah thats about it

- anonymous

did you understand how to do it though

- anonymous

check out this example though of finding area of sectors....

##### 1 Attachment

- anonymous

so wouldnt that arc length be 90 degrees

- anonymous

i don't know why they wrote it that way but
length is measure in metres right
and angle is measure in degrees
so arc length = 90 degrees really does not make any sense

- anonymous

well my original answer was 12.57 based on those examples they gave me and knowing the arc length was 90 degrees...

- anonymous

oh by the way arc length is not equal to 70 degrees in the example
arc length is equal to 70/360*2*pie*r

- anonymous

So, to solve for its area, apply the formula of area of circle.
[A= pir^2]
Since radius is half of the diameter, then:
[A_(c ir c l e)=pi(4/2)^2=pi(2)^2=4pi]
Then, divide divide it by 4.
[A_(ACB)=(4pi)/4=pi]

- anonymous

i found this on the internet... it said the answer is pi

- anonymous

o that makes more sense actually
the total area of the circle is pie*r^2
and in our question our circle can be divided into 4 such sectors
so area of circle /4 = 3.14
this answer is actually the right one
i feel stupid :/

- anonymous

|dw:1378323702346:dw|

- anonymous

i figured where i went wrong
the arc length is indeed equal to 3.14
but the area of a circle is equal to (arc length*r)/2

Looking for something else?

Not the answer you are looking for? Search for more explanations.