anonymous
  • anonymous
Is Arc AB 90 degrees?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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anonymous
  • anonymous
|dw:1378320193232:dw|
anonymous
  • anonymous
since the diameter of the circle is 4cm the radius = 2cm

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anonymous
  • anonymous
yes but how will that help me find the arc AB
anonymous
  • anonymous
?
anonymous
  • anonymous
what is the circumference of the circle?
amistre64
  • amistre64
you dont need circumference to find area ....
anonymous
  • anonymous
|dw:1378320396866:dw|
anonymous
  • anonymous
let arc AB=x then circumference/4= x
anonymous
  • anonymous
did you see what i did there?
amistre64
  • amistre64
the picture is asking to find the area of the shaded portion; even tho the post alludes to some arc length ...
anonymous
  • anonymous
the circumference of the circle is 2*pie*r = 2*3.14*2 = 12.56 arc AB = 12.56/4 = 3.14
anonymous
  • anonymous
yes i know but in order to find the area of the shaded sector i need to know the arc length first
amistre64
  • amistre64
you do not need to know the arc length in order to define the area ...
amistre64
  • 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
  • anonymous
(arc lenth *pie*r)/360 = area
anonymous
  • anonymous
Arc of sector ACB = measurement of arc AB/360 degrees X pi X r^@
amistre64
  • amistre64
the measure of the angle is needed, not the length of the arc
amistre64
  • amistre64
\[\Large Area=\frac{\theta}{360}\pi r^2\]
anonymous
  • anonymous
@amistre64 there may be multiple ways to solve a problem
amistre64
  • 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
  • amistre64
it just seems like more effort than what its worth at the moment
anonymous
  • anonymous
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anonymous
  • 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
  • amistre64
fair enough :)
anonymous
  • anonymous
yes..its given in d fig.
anonymous
  • anonymous
@hello1213 did you get the answer
anonymous
  • anonymous
no because i dont know the arc length
anonymous
  • anonymous
in the fig. its shown its right angled so its 90degree...
anonymous
  • anonymous
arch length is 3.14 if you want to know how we got that, scroll up and read again
anonymous
  • 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
  • anonymous
A= arc jk/360 X 12.566
anonymous
  • 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
  • anonymous
does that make sense
anonymous
  • anonymous
yes... what is the area of the shaded sector... its not making sense im getting about 0.11
anonymous
  • 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
  • anonymous
ok hold on
anonymous
  • anonymous
about 19.7 in.^2
anonymous
  • anonymous
yeah thats about it
anonymous
  • anonymous
did you understand how to do it though
anonymous
  • anonymous
check out this example though of finding area of sectors....
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anonymous
  • anonymous
so wouldnt that arc length be 90 degrees
anonymous
  • 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
  • anonymous
well my original answer was 12.57 based on those examples they gave me and knowing the arc length was 90 degrees...
anonymous
  • 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
  • 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
  • anonymous
i found this on the internet... it said the answer is pi
anonymous
  • 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
  • anonymous
|dw:1378323702346:dw|
anonymous
  • 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

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