anonymous
  • anonymous
Give the coordinates of a shape that can be rotated about the y-axis to create a cylinder. Provide an explanation and proof for your answer to receive full credit. Please help.
Geometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
a rectangle
anonymous
  • anonymous
Yes, thank you. But how do I rotate the rectangle about the y-axis?
anonymous
  • anonymous
take the integral with respect to the y-axis. For example if the rectangle was the region between the y-axis and the line x=5

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anonymous
  • anonymous
Yes, thank you. But how do I rotate the rectangle about the y-axis?
anonymous
  • anonymous
I'm not sure what you're asking
anonymous
  • anonymous
Sorry, my computer just acted up and reloaded, sending my last post again. What is an integral?
anonymous
  • anonymous
what subject are you in? I assumed you were doing calculus, but I guess not?
anonymous
  • anonymous
No, I am in Geometry.
anonymous
  • anonymous
to make the cylinder we need to rotate a vertical line around the y-axis. http://image.tutorvista.com/content/feed/u839/Solid%20of%20revolution.PNG Basically the y-axis is the center of rotation, meaning it doesn't move, and the line revolves around it 360° in a full circle
anonymous
  • anonymous
So the coordinates are rotating 360 degrees. If my coordinate is (2,0) what would the new coordinate as a result of the rotation?
anonymous
  • anonymous
(2, 0). 360° is all the way around so you end up where you started.
anonymous
  • anonymous
I tend to use revolve and rotate interchangeably. I think revolve would be more accurate here, so where revolving around the y-axis. |dw:1433296347093:dw|
anonymous
  • anonymous
Ahh so if my understanding is correct, then I can choose any 4 coordinates as long as they create a rectangle. Undergoing the 360 degree rotation, the transformed coordinates about the y-axis would be exactly the same as the original?
anonymous
  • anonymous
I think we're referring to two different things. |dw:1433296702076:dw|
anonymous
  • anonymous
Ahh okay. So how do I go about answering this question?
anonymous
  • anonymous
Pick 4 points for the rectangle, and put two of them on the y-axis to keep it simple. For a proof, use the formula for the volume of a cylinder, V = πr²h. A more general equation for volume of any shape is V = Ah, where A is the cross-sectional area. For a cylinder, the cross-sectional area is the circle on top. |dw:1433297282078:dw|
anonymous
  • anonymous
The volume of the revolved rectangle will be V = πw²h, and since w is the radius of the cylinder, V = πr²h, which is the volume of a cylinder
anonymous
  • anonymous
Would these coordinates work? (0,0) ; (2,0) ; (2,6) ; (0,6)
anonymous
  • anonymous
yes
anonymous
  • anonymous
Okay, I understand the answer thoroughly now. Thank you so much for your time and knowledge. Are there any rewards I can give you on this site? I am new to Open Study.
anonymous
  • anonymous
You're welcome. I'd appreciate it if you gave a medal using the best response button.
anonymous
  • anonymous
Should I click best response for each of your posts?
anonymous
  • anonymous
No. Any one of them will do it.
anonymous
  • anonymous
Thank you!
anonymous
  • anonymous
No, thank you! Have a nice evening.
anonymous
  • anonymous
You too.

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