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AdhaZeera Group Title

What area can the goat roam?

  • 2 years ago
  • 2 years ago

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  1. AdhaZeera Group Title
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    |dw:1350884315409:dw|

    • 2 years ago
  2. AdhaZeera Group Title
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    Fence SHED 4feet 5feet 8feet

    • 2 years ago
  3. UnkleRhaukus Group Title
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    |dw:1350884748553:dw|

    • 2 years ago
  4. UnkleRhaukus Group Title
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    ops i dident see the fence

    • 2 years ago
  5. Fellowroot Group Title
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    Can he go inside the shed? And is he/she connected by a chain that is connected to the corner of the shed?

    • 2 years ago
  6. UnkleRhaukus Group Title
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    |dw:1350884878590:dw|

    • 2 years ago
  7. AdhaZeera Group Title
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    No he's not connected. I'm not sure. That's all my teacher wrote

    • 2 years ago
  8. Fellowroot Group Title
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    he has to be connected by a chain to the shed right?

    • 2 years ago
  9. AdhaZeera Group Title
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    Wait... yes..

    • 2 years ago
  10. UnkleRhaukus Group Title
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    |dw:1350885122452:dw|

    • 2 years ago
  11. UnkleRhaukus Group Title
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    |dw:1350885496696:dw|

    • 2 years ago
  12. AdhaZeera Group Title
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    How do I calculate it?

    • 2 years ago
  13. UnkleRhaukus Group Title
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    break the shape in to smaller shapes

    • 2 years ago
  14. Fellowroot Group Title
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    Unkle Rhaukus I like your drawings, but what is the actual value?

    • 2 years ago
  15. AdhaZeera Group Title
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    81 sq ft??

    • 2 years ago
  16. Fellowroot Group Title
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    I'm very sure I know how to do it. Just give me some time to work it out.

    • 2 years ago
  17. Fellowroot Group Title
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    its not easy, but i'm still working.

    • 2 years ago
  18. Fellowroot Group Title
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    Ok, here it comes. Writing it up. :) !!!!!

    • 2 years ago
  19. AdhaZeera Group Title
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    You there?

    • 2 years ago
  20. Fellowroot Group Title
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    yeah hang on almost done

    • 2 years ago
  21. Fellowroot Group Title
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    you might be surprised but i got it.

    • 2 years ago
  22. Fellowroot Group Title
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    GOT IT!!!!

    • 2 years ago
  23. UnkleRhaukus Group Title
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    im not sure why you had to integrate

    • 2 years ago
  24. AdhaZeera Group Title
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    Thank you!

    • 2 years ago
  25. UnkleRhaukus Group Title
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    we know the are of a circle is πr^2, so a semicircle has area (πr^2)/2 and a quater circle has area (πr^2)/4

    • 2 years ago
  26. Fellowroot Group Title
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    I integrated because I wanted to take the whole circle and then subtract the parts where the goat can't go. The area of the top of the circle is curved and the goat can't go there. So I created a function and integrated it so that I could find that exact area that is fenced off.

    • 2 years ago
  27. UnkleRhaukus Group Title
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    |dw:1350888457508:dw|

    • 2 years ago
  28. Fellowroot Group Title
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    @ AdhaZeera Do you understand what I did when I integrated. I will explain it to you if you want. I used calculus to arrive at that answer.

    • 2 years ago
  29. UnkleRhaukus Group Title
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    |dw:1350888515709:dw|

    • 2 years ago
  30. UnkleRhaukus Group Title
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    the sector is 1/12 of a circle

    • 2 years ago
  31. Fellowroot Group Title
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    @ UnkleRhaukus I know that there is a formula that is A= (theta)r^2/2 but I don't how it works here.

    • 2 years ago
  32. UnkleRhaukus Group Title
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    \[A=\frac{\pi\times 3^2}4+\frac{\pi \times8^2}{2}+\frac{\pi \times8^2}{12}+\frac{4\times 8}{2}\]\[=\pi\times\frac{465}{12}+16\]\[\approx 140\]

    • 2 years ago
  33. UnkleRhaukus Group Title
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    well theta was 30° right? angles of segment / angle in circle \[30°/360°=1/12\] area of segment / area of circle \[\frac{\pi r^2}{12}\qquad/\qquad\pi r^2\]

    • 2 years ago
  34. UnkleRhaukus Group Title
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    i had to use a trig ratio to to get 30° btw

    • 2 years ago
  35. Fellowroot Group Title
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    Your value comes to 140.35 mine is 141.7, its off only by a hair and is a very good approximation, but mine is exact.

    • 2 years ago
  36. UnkleRhaukus Group Title
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    where did i error?

    • 2 years ago
  37. Fellowroot Group Title
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    not sure, but its pretty darn good.

    • 2 years ago
  38. UnkleRhaukus Group Title
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    \[A=\frac{\pi\times 3^2}4+\frac{\pi \times8^2}{2}+\frac{\pi \times8^2}{12}+\frac{4\times 8}{2}=\pi\times\frac{475}{12}+16\approx140.35\]

    • 2 years ago
  39. UnkleRhaukus Group Title
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    @Fellowroot i think we got different answers because we were solving different regions our pictures are different

    • 2 years ago
  40. Fellowroot Group Title
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    |dw:1350891993500:dw| The only thing I don't know if that if the 5 feet fence touches the edge of the circle or if there is a gab. For the solution i provided it doesn't matter though. On my pic, the 'x', I really don't know that distance, it may make a difference for your answer, i don't know.

    • 2 years ago