anonymous
  • anonymous
PLEASE PLEASE HELP! A circle has a radius of 8 inches. Find the area of a sector of the circle if the sector has an arc that measures 45°. 2 sq. in.? 8 sq. in.? 16 sq. in.?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Its 8 nches right?
Yttrium
  • Yttrium
Do you know the formula in finding the are of a sector?
Yttrium
  • Yttrium
I mean area

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More answers

nubeer
  • nubeer
You should start by converting the angle 45 into radian.. then formula for area is = 0.5*r^2* theta.. theta is the angle here.. you have the radius too given in the question.. so just plug in the values.
Yttrium
  • Yttrium
The formula for finding the length of the sector:\[s = r theta\] For the area of a sector: \[A = (1/2) r ^{2} \theta\]
anonymous
  • anonymous
We work with dragee !
Yttrium
  • Yttrium
Well, nubeer is right. It must be converted first into radian.
nubeer
  • nubeer
nop @E.ali .. we do these kind of problems in radian.. these formula can be applied when angle is in radian.
anonymous
  • anonymous
We can work with cm and dragee ! Ha ?!:)
anonymous
  • anonymous
@ nubeer ,8 in = cm ?
nubeer
  • nubeer
doesn't matter if it's in cm or in.. it would work for both.. we just have to see for the angle.. if it's in radian or degree.
anonymous
  • anonymous
Thank you guys
nubeer
  • nubeer
but if u wanna know.. 1 inch = 2.5 cm
anonymous
  • anonymous
If we work with Cm shold work with Dragee to and if work with in should work with Radian too !
anonymous
  • anonymous
first of all, let's just make sure we understand the terminology, a sector is basically like a slice of the circle cut from the center out, like a slice of pie and the measure of the arc is the same as the measure of the central angle
anonymous
  • anonymous
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anonymous
  • anonymous
so when we say an arc has a measure of 45 degrees, we're really talking about the angle at the center of the circle, what we really need to do to get the area of the sector (the slice), is figure out what fraction of the circle that slice is, and then multiply that fraction by the area of the whole circle.
anonymous
  • anonymous
45/360 is the part of circle 8in=20cm S c = r^2.314/100.part of circle S c = 4 . 314 . 1/8 S c = 1/2 . 314 S c = 157 cm^2 157 cm^2 = ?in
anonymous
  • anonymous
one easy way to figure out what fraction of a circle that sector is, is to look at the angle.
anonymous
  • anonymous
so we can just compare our arc, or central angle, of 45 degrees to 360 degrees, to get our fraction so just reduce 45/360 which gives us 1/8. So now we know that the sector with the 45 degree arc is 1/8 of the circle so it has 1/8 the area of the circle so just calculate the area of the circle and divide by 8. do you remember the area formula for a circle, well since your not online I will have to tell. So its pi r^2. and unless they tell you to approximate pi, they probably want you to keep pi in your answer, so the answer is exact.
anonymous
  • anonymous
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anonymous
  • anonymous
|dw:1377935177517:dw|
anonymous
  • anonymous
in this case 8 pi square inches, is our answer. I hope my working outs helped you understand this problem, once your online please leave a comment so I know you understood. Thanks! :)

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