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Math Help - Radian measure

  1. #1
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    Radian measure

    The diagram shows a sector OAB of a circle, centre O and radius r cm. The length of the arc AB is p cm and angle AOB is Ѳ radian.

    (a) Find Ѳ in terms of p & r.
    (b) Deduce that the area of the sector is 1/2pr cm^2.

    Given that r = 4.7 and p = 5.3, where each has been measured to 1 decimal place, find, giving your answer to 3 decimal places:
    (c) The least possible value of the area of a sector.
    (d) The range of possible values of Ѳ.
    ------------------------------------------------

    I don’t understand this question properly. What is the least possible value? And what is the range?

    By taking given r & p's value,

    A = * (4.7)^2 * (5.3/4.7) [Using A = 1/2 * r^2 * Ѳ]
    = 12.455 cm^2

    But book’s answer: 12.206 cm^2.
    Attached Thumbnails Attached Thumbnails Radian measure-c2.6d.5.bmp  
    Last edited by geton; November 23rd 2008 at 04:42 AM. Reason: Sketch added + full que
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  2. #2
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    your calculation is correct.

    is this the entire problem as written in the text?
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  3. #3
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    Quote Originally Posted by skeeter View Post
    your calculation is correct.

    is this the entire problem as written in the text?
    I edited my question with full text.
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  4. #4
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    "Given that r = 4.7 and p = 5.3, where each has been measured to 1 decimal place"

    That means the least possible value of r = 4.65 and the least possible value of p = 5.25

    Now, 1/2 * p * r = 1/2 * 5.25 * 4.65 = 12.206 cm^2 ---> Book's answer

    You know the least possible values of r and p. The maximum possible value of r = 4.74 and p = 5.34. Now can you find the range of values of theta?

    I hope that helps.

    ILoveMaths07.
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  5. #5
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    Quote Originally Posted by ILoveMaths07 View Post
    "Given that r = 4.7 and p = 5.3, where each has been measured to 1 decimal place"

    That means the least possible value of r = 4.65 and the least possible value of p = 5.25

    Now, 1/2 * p * r = 1/2 * 5.25 * 4.65 = 12.206 cm^2 ---> Book's answer

    You know the least possible values of r and p. The maximum possible value of r = 4.74 and p = 5.34. Now can you find the range of values of theta?

    I hope that helps.

    ILoveMaths07.

    Thank you
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