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anonymous

  • one year ago

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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  1. anonymous
    • one year ago
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    42 Square units. :)

  2. campbell_st
    • one year ago
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    you are after arc length... not area

  3. anonymous
    • one year ago
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    Lol thank you , but that choice isnt up there.

  4. campbell_st
    • one year ago
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    what fraction of the circle does an angle of 120 form..?

  5. anonymous
    • one year ago
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    wait what?

  6. campbell_st
    • one year ago
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    so an angle of 120 if what fraction of the circle... or revolution...?

  7. anonymous
    • one year ago
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    idk

  8. campbell_st
    • one year ago
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    ok... here is what you need |dw:1434486024769:dw| a circle is 360 degrees so \[Arc ~Length = \frac{\theta}{360} \times 2 \pi r\]

  9. anonymous
    • one year ago
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    well 180 X 2 = 360

  10. campbell_st
    • one year ago
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    |dw:1434486216085:dw|

  11. anonymous
    • one year ago
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    this is so confusing , i just dont understand this question period.

  12. campbell_st
    • one year ago
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    ok... so you have learnt about the circumference of a circle..?

  13. anonymous
    • one year ago
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    its the area of a circle right?

  14. campbell_st
    • one year ago
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    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 \[\frac{Central ~Angle}{360}\]

  15. campbell_st
    • one year ago
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    the question is asking for arc length... so the area formula doesn't work. You need circumference.

  16. anonymous
    • one year ago
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    Like i said 9.42 Square units

  17. anonymous
    • one year ago
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    at the beginning

  18. campbell_st
    • one year ago
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    you are asked for a linear measurement... not an area... so eliminate choice 3.

  19. anonymous
    • one year ago
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    campbell my mom got aids from you enough with the boring lectures

  20. anonymous
    • one year ago
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    so the answers 9.42?

  21. campbell_st
    • one year ago
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    if you think 9.42 is the answer... then choose it...

  22. anonymous
    • one year ago
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    omg i need help , so i dont pick the wrong answer

  23. campbell_st
    • one year ago
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    well step 1 do you know how to find the circumference of a circle with radius 3 units?

  24. anonymous
    • one year ago
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    no

  25. campbell_st
    • one year ago
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    ok...do you know what the circumference of a circle is

  26. anonymous
    • one year ago
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    the distance around a circle

  27. campbell_st
    • one year ago
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    great... and an arc is part of the distance... does that make sense...?

  28. anonymous
    • one year ago
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    ummm not really.

  29. campbell_st
    • one year ago
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    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...

  30. campbell_st
    • one year ago
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    that's the 1st part of the problem

  31. campbell_st
    • one year ago
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    what answer did you get..?

  32. anonymous
    • one year ago
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    18.84

  33. campbell_st
    • one year ago
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    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 \[\frac{120}{360}\]

  34. campbell_st
    • one year ago
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    Arc Length = fraction x circumference

  35. anonymous
    • one year ago
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    1/3

  36. campbell_st
    • one year ago
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    great so the arc length is 1/3 of 18.84 what do you get...?

  37. campbell_st
    • one year ago
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    so just do 18.84/3 =

  38. anonymous
    • one year ago
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    6.28

  39. campbell_st
    • one year ago
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    is that an answer choice..?

  40. anonymous
    • one year ago
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    Yes , thank you.

  41. campbell_st
    • one year ago
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    glad it helped

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