anonymous
  • anonymous
A central angle measuring 120° intercepts an arc in a circle whose radius is 3. What is length of the arc of the circle formed by this central angle? Round the length of the arc to the nearest hundredth of unit. 6.28 units 12.57 units 9.42 square units 6.28 degrees
Mathematics
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anonymous
  • anonymous
A central angle measuring 120° intercepts an arc in a circle whose radius is 3. What is length of the arc of the circle formed by this central angle? Round the length of the arc to the nearest hundredth of unit. 6.28 units 12.57 units 9.42 square units 6.28 degrees
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
42 Square units. :)
campbell_st
  • campbell_st
you are after arc length... not area
anonymous
  • anonymous
Lol thank you , but that choice isnt up there.

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campbell_st
  • campbell_st
what fraction of the circle does an angle of 120 form..?
anonymous
  • anonymous
wait what?
campbell_st
  • campbell_st
so an angle of 120 if what fraction of the circle... or revolution...?
anonymous
  • anonymous
idk
campbell_st
  • campbell_st
ok... here is what you need |dw:1434486024769:dw| a circle is 360 degrees so \[Arc ~Length = \frac{\theta}{360} \times 2 \pi r\]
anonymous
  • anonymous
well 180 X 2 = 360
campbell_st
  • campbell_st
|dw:1434486216085:dw|
anonymous
  • anonymous
this is so confusing , i just dont understand this question period.
campbell_st
  • campbell_st
ok... so you have learnt about the circumference of a circle..?
anonymous
  • anonymous
its the area of a circle right?
campbell_st
  • campbell_st
the arc length is simply the circumference of the whole circle multiplied by the fraction of the circle you are dealing with. so the fraction is \[\frac{Central ~Angle}{360}\]
campbell_st
  • campbell_st
the question is asking for arc length... so the area formula doesn't work. You need circumference.
anonymous
  • anonymous
Like i said 9.42 Square units
anonymous
  • anonymous
at the beginning
campbell_st
  • campbell_st
you are asked for a linear measurement... not an area... so eliminate choice 3.
anonymous
  • anonymous
campbell my mom got aids from you enough with the boring lectures
anonymous
  • anonymous
so the answers 9.42?
campbell_st
  • campbell_st
if you think 9.42 is the answer... then choose it...
anonymous
  • anonymous
omg i need help , so i dont pick the wrong answer
campbell_st
  • campbell_st
well step 1 do you know how to find the circumference of a circle with radius 3 units?
anonymous
  • anonymous
no
campbell_st
  • campbell_st
ok...do you know what the circumference of a circle is
anonymous
  • anonymous
the distance around a circle
campbell_st
  • campbell_st
great... and an arc is part of the distance... does that make sense...?
anonymous
  • anonymous
ummm not really.
campbell_st
  • campbell_st
ok... a fact to remember is that an arc is part of the circumference of a circle... the formula for circumference is \[C = 2 \times \pi \times r\] C = Circumference, r = radius... and pi is a constant = 3.14 so you know r =3 just substitute it and find the circumference...
campbell_st
  • campbell_st
that's the 1st part of the problem
campbell_st
  • campbell_st
what answer did you get..?
anonymous
  • anonymous
18.84
campbell_st
  • campbell_st
great so the distance around the whole circle is 18.84 units now the central angle is 120 degrees a circle contains 360 degrees so simplify the fraction \[\frac{120}{360}\]
campbell_st
  • campbell_st
Arc Length = fraction x circumference
anonymous
  • anonymous
1/3
campbell_st
  • campbell_st
great so the arc length is 1/3 of 18.84 what do you get...?
campbell_st
  • campbell_st
so just do 18.84/3 =
anonymous
  • anonymous
6.28
campbell_st
  • campbell_st
is that an answer choice..?
anonymous
  • anonymous
Yes , thank you.
campbell_st
  • campbell_st
glad it helped

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