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Math Help - area of a circle in a square

  1. #1
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    area of a circle in a square

    i have been given a question and i don't know how to work it out please help. green line is 3 cm and red line is cm the circle is supposed to just be touching the square, i might have put something wrong but it is about this help...
    area of a circle in a square-problem.jpg
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  2. #2
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    You forgot length of red line...
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  3. #3
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    oh yeah sorry it is 6
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  4. #4
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    i meant 6
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  5. #5
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    You could use Pythagoras' theorem

    R^2=(R-6)^2+(R-3)^2

    R^2=R^2-12R+36+R^2-6R+9

    R^2-18R+45=0

    (R-3)(R-15)=0
    Attached Thumbnails Attached Thumbnails area of a circle in a square-pythagoras-mhf.jpg  
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  6. #6
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    oh cheers archie, what would that make the area of the circle
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  7. #7
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    Now that you get R (the smart choice from the factors), plug it into the circle area formula

    A={\pi}R^2
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  8. #8
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    so what is r ?
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  9. #9
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    Have a think about it.
    The background to this is being able to factor a quadratic
    and discover the solution of the radius from the factors.

    Then use the radius to calculate circle area.
    You need to know this.
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  10. #10
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    so r = 25 ??????????
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  11. #11
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    You didn't think for very long !

    Have a look at the factors.
    When you multiply them, the answer is zero.
    So, either factor is zero for a certain value of R.
    What values of R make those factors 0 ?
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  12. #12
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    so the two numbers need to multiply to 45 and add to 18 so 15 and 3 again?
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  13. #13
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    Quote Originally Posted by kitobeirens View Post
    so the two numbers need to multiply to 45 and add to 18 so 15 and 3 again?
    Yes, that's how the quadratic was factored.

    Now the two factors in brackets give you the answers visually.

    What is R-15 if R=15 and what is R-3 if R=3 ?
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  14. #14
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    Kito, since you obviously don't understand how the quadratic formula works,
    then you are not ready for this problem. Suggest you talk to your math teacher.
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  15. #15
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    oh its 15 isnt it because 15 squared =225 -(18x15=270) so 225-270+45=0
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