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xRAWRRx3

  • 3 years ago

Please help. :( In the figure below, rectangle ABCD is rotated about side AB. If Ab = 10 and BC = 4 , what is the volume of the resulting solid?

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  1. xRAWRRx3
    • 3 years ago
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    |dw:1338516177766:dw|

  2. jim_thompson5910
    • 3 years ago
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    First, it helps to figure out what solid figure you'll get if you rotate this

  3. jim_thompson5910
    • 3 years ago
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    Any ideas of what type of solid figure it will be?

  4. xRAWRRx3
    • 3 years ago
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    i have no clue.

  5. jim_thompson5910
    • 3 years ago
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    Imagine spinning this around AB (think of AB as stuck to the ground) and this rectangle is like a door. What you'll get is a cylinder.

  6. xRAWRRx3
    • 3 years ago
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    How'd you get that? Is that like common sense or something?

  7. jim_thompson5910
    • 3 years ago
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    I'm imagining it in my mind really, but you can grab a rectangular object and spin it along a side. You'll see that it traces out a cylinder.

  8. xRAWRRx3
    • 3 years ago
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    then i guess by rotates they mean folded kinda??

  9. xRAWRRx3
    • 3 years ago
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    **rotated

  10. xRAWRRx3
    • 3 years ago
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    like rolled up?

  11. jim_thompson5910
    • 3 years ago
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    no it's not folding in any way

  12. jim_thompson5910
    • 3 years ago
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    one moment while I track down an animation of this

  13. xRAWRRx3
    • 3 years ago
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    okay, thank you.

  14. jim_thompson5910
    • 3 years ago
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    hmm not finding much sadly, but think of a propeller blade

  15. xRAWRRx3
    • 3 years ago
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    It's alright. I got it. so what do i do after?

  16. jim_thompson5910
    • 3 years ago
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    When it's not moving, it's in one spot...but when it spins, it resembles a circle correct?

  17. xRAWRRx3
    • 3 years ago
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    Oh. Okay. So its a cyclinder. what do i do after?

  18. jim_thompson5910
    • 3 years ago
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    what's the height of the cylinder?

  19. xRAWRRx3
    • 3 years ago
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    10.

  20. jim_thompson5910
    • 3 years ago
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    and what's the radius of the top of the cylinder?

  21. xRAWRRx3
    • 3 years ago
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    but isn't the circumference 4?

  22. xRAWRRx3
    • 3 years ago
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    since the whole side BC is 4?

  23. jim_thompson5910
    • 3 years ago
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    that's not the circumference

  24. jim_thompson5910
    • 3 years ago
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    that's actually the radius since that's as far as it goes in that direction

  25. jim_thompson5910
    • 3 years ago
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    |dw:1338517802914:dw|

  26. jim_thompson5910
    • 3 years ago
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    |dw:1338517841316:dw|

  27. jim_thompson5910
    • 3 years ago
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    The rectangle will rotate about that dotted line (which is AB) to create that cylinder. So that's why the radius is 4.

  28. xRAWRRx3
    • 3 years ago
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    I don't really get how its four...

  29. jim_thompson5910
    • 3 years ago
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    Do you see how that cylinder is created?

  30. xRAWRRx3
    • 3 years ago
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    how'd you get it? i still dont get how you created the cylinder like that..

  31. jim_thompson5910
    • 3 years ago
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    I spun the rectangle around that dotted line. The cylinder represents the space that the rectangle carves out (think of the spinning rectangle as a saw or drill cutting into wood)

  32. xRAWRRx3
    • 3 years ago
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    but how is the radius 4? wouldn't it be 2?

  33. jim_thompson5910
    • 3 years ago
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    no, the radius is shown in the next drawing |dw:1338519158344:dw|

  34. jim_thompson5910
    • 3 years ago
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    and that length is exactly the length of BC

  35. xRAWRRx3
    • 3 years ago
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    oh, so AB stays in one spot and The rest of the rectangle kinda like spun around to make the cylinder?

  36. jim_thompson5910
    • 3 years ago
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    exactly, AB never move at all but the other points spin/move around

  37. jim_thompson5910
    • 3 years ago
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    A and B never move as well

  38. xRAWRRx3
    • 3 years ago
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    ohhh, i get it. so is the answer 160 pi?

  39. jim_thompson5910
    • 3 years ago
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    you nailed it

  40. xRAWRRx3
    • 3 years ago
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    Yay :) thank you so much x)

  41. jim_thompson5910
    • 3 years ago
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    you're welcome

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