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anonymous

  • one year ago

The base of a solid in the xy-plane is the circle x2 + y2 = 16. Cross sections of the solid perpendicular to the y-axis are equilateral triangles. What is the volume, in cubic units, of the solid?

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  1. DanJS
    • one year ago
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    Do you know what the solid is?

  2. anonymous
    • one year ago
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    no I don't know how to start this problem

  3. DanJS
    • one year ago
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    |dw:1438722075391:dw|

  4. DanJS
    • one year ago
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    They gave you x^2 + y^2 = 16 = r^2 That is a circle radius 4 centered at the origin, in the XY-plane...

  5. DanJS
    • one year ago
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    you recognize that?

  6. anonymous
    • one year ago
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    yes

  7. DanJS
    • one year ago
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    |dw:1438722233544:dw|

  8. DanJS
    • one year ago
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    bad drawing, but that is a slice of the shape perpendicular to the Y axis

  9. DanJS
    • one year ago
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    saying it is equilateral, means that is a Right Circular Cone

  10. anonymous
    • one year ago
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    okay so you need the volume formula for a right circular cone correct?

  11. DanJS
    • one year ago
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    yes, just remember, it is the area of the base times 1/3 the height

  12. anonymous
    • one year ago
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    ok

  13. DanJS
    • one year ago
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    need to figure the height

  14. DanJS
    • one year ago
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    Loooking at the cross section at the XZ axis head on... the base is 2 times the radius

  15. DanJS
    • one year ago
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    |dw:1438722512573:dw|

  16. DanJS
    • one year ago
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    THe y axis is pointing out from the page, that is the origin

  17. DanJS
    • one year ago
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    Equilateral triangle, so the diagonals are the same as the base, 2 radiuses

  18. DanJS
    • one year ago
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    radii

  19. DanJS
    • one year ago
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    r=4, use pythagorean theorem to figure the height

  20. DanJS
    • one year ago
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    |dw:1438722659628:dw|

  21. DanJS
    • one year ago
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    You get it all?

  22. anonymous
    • one year ago
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    yes so far

  23. DanJS
    • one year ago
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    |dw:1438722796113:dw|

  24. DanJS
    • one year ago
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    you can only put in the 2r because they told you the cross sections are equilateral

  25. DanJS
    • one year ago
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    |dw:1438722884153:dw|

  26. DanJS
    • one year ago
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    pelletty drawing, but hope you see where those measurments come from

  27. anonymous
    • one year ago
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    yes it is understood

  28. DanJS
    • one year ago
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    k, so you know the radius and height, you can calculate the volume \[V = \frac{ 1 }{ 3 }\pi*r^2*h\]

  29. DanJS
    • one year ago
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    r = 4 h = sqrt(8^2 - 4^2)

  30. anonymous
    • one year ago
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    The way you set it up is multiply 1/3 by pi(4)^2(sqrt(8^2-4^2))?

  31. DanJS
    • one year ago
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    yes, if you simplify the height first, it is... \[h = \sqrt{64-16} = 4\sqrt{3}\]

  32. anonymous
    • one year ago
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    okay thank you very much for the explanation

  33. DanJS
    • one year ago
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    \[V = \frac{ 1 }{ 3 }*\pi*4^2*4\sqrt{3}\]

  34. DanJS
    • one year ago
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    welcome, that was a fun prob.. hope ya get it

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