Volume Question - shell method (1 Viewer)

asb_92

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oki.. so i hav a test on volumes in 2 days.. and i dnt get how teh heckk i gta do this stufff >< can soemone plz help me out with this qu?

The area enclosed by y=x^2 and x=y^2 is rotated about y-axis. Find the volume.

thanks veryy muchh!
and also if u guys have any tips on how to approach volumes questions and stuff?

thanks again :D
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Drongoski

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The 2 curves intersect @ (0,0) and (1,1)





Don't know if answer is right.
 

Aerath

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I got 3pi/10 too. But just make sure you're using shell method [I'm not quite sure Drongoski used it].
 

Drongoski

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I got 3pi/10 too. But just make sure you're using shell method [I'm not quite sure Drongoski used it].
You are right. I forgot and was hurrying off to tutor.
 
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Drongoski

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Cylindrical Shells Version


 
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asb_92

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im confused..
could u please explain how u got to the answer?:S

haha im a losty when it comes to mathh ><
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Drongoski

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im confused..
could u please explain how u got to the answer?:S

haha im a losty when it comes to mathh ><
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which part are u not clear about ?
 

asb_92

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the 2pi x( y2 - y1) part...:S
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Drongoski

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Take a typical very thin vertical strip, of thickness delta x, of the area between the 2 curves; when spinned around the Y-axis, it forms a cylindrical shell, of radius x, and of height given by the 'y' of the upper curve minus the 'y' of the lower curve (y=x^2).

The circumference of a circle radius r is 2 x pi x r (for this question, it is "2 pi x" ); multiply this by the height (sqrt(x) - x^2) times delta x (like dx) gives you the volume of this thin cylinder. The total volume comes from adding up all these thin cylindrical shells, all the way from x=0 to x=1. This is roughly what the integral is all about.

Hope this helps.
 

asb_92

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http://community.boredofstudies.org/members/drongoski/
thanks heappsss!! that helped a lott!!! Drongoski :D:D
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