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anonymous
 one year ago
Give the coordinates of a shape that can be rotated about the yaxis to create a cylinder. Provide an explanation and proof for your answer to receive full credit. Please help.
anonymous
 one year ago
Give the coordinates of a shape that can be rotated about the yaxis to create a cylinder. Provide an explanation and proof for your answer to receive full credit. Please help.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, thank you. But how do I rotate the rectangle about the yaxis?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0take the integral with respect to the yaxis. For example if the rectangle was the region between the yaxis and the line x=5

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, thank you. But how do I rotate the rectangle about the yaxis?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure what you're asking

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, my computer just acted up and reloaded, sending my last post again. What is an integral?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what subject are you in? I assumed you were doing calculus, but I guess not?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, I am in Geometry.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to make the cylinder we need to rotate a vertical line around the yaxis. http://image.tutorvista.com/content/feed/u839/Solid%20of%20revolution.PNG Basically the yaxis is the center of rotation, meaning it doesn't move, and the line revolves around it 360° in a full circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the coordinates are rotating 360 degrees. If my coordinate is (2,0) what would the new coordinate as a result of the rotation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(2, 0). 360° is all the way around so you end up where you started.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I tend to use revolve and rotate interchangeably. I think revolve would be more accurate here, so where revolving around the yaxis. dw:1433296347093:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahh 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 yaxis would be exactly the same as the original?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think we're referring to two different things. dw:1433296702076:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ahh okay. So how do I go about answering this question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Pick 4 points for the rectangle, and put two of them on the yaxis 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 crosssectional area. For a cylinder, the crosssectional area is the circle on top. dw:1433297282078:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The 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
 one year ago
Best ResponseYou've already chosen the best response.0Would these coordinates work? (0,0) ; (2,0) ; (2,6) ; (0,6)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, 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
 one year ago
Best ResponseYou've already chosen the best response.0You're welcome. I'd appreciate it if you gave a medal using the best response button.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Should I click best response for each of your posts?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No. Any one of them will do it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, thank you! Have a nice evening.
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