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

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- anonymous

42 Square units. :)

- campbell_st

you are after arc length... not area

- anonymous

Lol thank you , but that choice isnt up there.

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## More answers

- campbell_st

what fraction of the circle does an angle of 120 form..?

- anonymous

wait what?

- campbell_st

so an angle of 120 if what fraction of the circle... or revolution...?

- anonymous

idk

- 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

well 180 X 2 = 360

- campbell_st

|dw:1434486216085:dw|

- anonymous

this is so confusing , i just dont understand this question period.

- campbell_st

ok... so you have learnt about the circumference of a circle..?

- anonymous

its the area of a circle right?

- 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

the question is asking for arc length... so the area formula doesn't work. You need circumference.

- anonymous

Like i said 9.42 Square units

- anonymous

at the beginning

- campbell_st

you are asked for a linear measurement... not an area... so eliminate choice 3.

- anonymous

campbell my mom got aids from you enough with the boring lectures

- anonymous

so the answers 9.42?

- campbell_st

if you think 9.42 is the answer... then choose it...

- anonymous

omg i need help , so i dont pick the wrong answer

- campbell_st

well step 1
do you know how to find the circumference of a circle with radius 3 units?

- anonymous

no

- campbell_st

ok...do you know what the circumference of a circle is

- anonymous

the distance around a circle

- campbell_st

great... and an arc is part of the distance... does that make sense...?

- anonymous

ummm not really.

- 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

that's the 1st part of the problem

- campbell_st

what answer did you get..?

- anonymous

18.84

- 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

Arc Length = fraction x circumference

- anonymous

1/3

- campbell_st

great so the arc length is 1/3 of 18.84
what do you get...?

- campbell_st

so just do 18.84/3 =

- anonymous

6.28

- campbell_st

is that an answer choice..?

- anonymous

Yes , thank you.

- campbell_st

glad it helped

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