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Solids of Revolution around y = x 
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#1
Feb513, 04:10 PM

P: 100

Is it possible to revolve a function around y = x? If so how would you do it?
I suppose the main difficulty is in finding the radius for the area of a disk or cylinder. Is there any method that works will all or most functions? 


#2
Feb513, 04:52 PM

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Hi TheAbsoluTurk!
Easiest way is to change to new coordinates p = x + y, q = x  y (or the same but divided by √2, if you prefer). Then x = y is the q axis, so that's just a rotation about the q axis. 


#3
Feb513, 05:25 PM

P: 100

p = x + y q = x  y So do I have to insert (q + y) into x to make y = (q + y)^2 ? 


#4
Feb513, 05:35 PM

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Solids of Revolution around y = x
Easier is to substitute x = (p+q)/2, y = (pq)/2



#5
Feb513, 05:44 PM

P: 100




#6
Feb513, 05:49 PM

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uhh?
just do it … substitute those formulas into y = x^{2} ! 


#7
Feb513, 05:53 PM

P: 100




#8
Feb513, 06:01 PM

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P: 26,148

your axis (originally called x=y) is the q axis, so r is the distance from the q axis, which is p (or is it p/2?) 


#9
Feb513, 06:26 PM

P: 100

What is the volume of y = x^2 rotated about y = x? Define p = x +y Define q = x  y I don't understand why you chose to insert x = (p+q)/2 and y = (pq)/2 ? How did you get these? 


#10
Feb513, 08:17 PM

P: 100




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