February 15th, 2011, 06:48 AM  #1 
Newbie Joined: Feb 2011 Posts: 2 Thanks: 0  Please Help......Volume Disk
Please check why my answers are wrong, I don't know what has I done wrong. Thank you so much. 1)FInd the volume of the solid that results when the region enclosed by x=sqrt(y), and x=y/4 is revolved about the xaxis. [color=#0000FF]My Steps: y=sqrt(x), y=x/4 [/color][color=#FF0000](switch x and y)[/color] [color=#0000FF]V=pi ?( [sqrt(x)]^2 (x/4)^2 dx); from 0 to 16 V=pi ?( x  (x^2)/16 dx); from 0 to 16 V=33.510 units^3 [/color] (correct answer: 428.032 units^3) 2)Find the volume of the solid that results when the region enclosed by y=sqrt(x), y=0, and x=9 is revolved about the line x=9. [color=#0000FF]My Steps: V=pi ?( [sqrt(x)]^2 dx); from 0 to 9 V=pi ?( x dx); from 0 to 9 V=127.234 units^3[/color] (correct answer: 407.150units^3) 3)Find the volume of the solid that results when the region enclosed by x=y^2 and x=y is revolved about the line y=1. My Steps: [color=#0000FF]y=x^2, y=x, revolved at x=1 [/color][color=#FF0000](switch x and y)[/color] [color=#0000FF]V=pi ?( [(x+1)^2]  [(x^2)+1]^2 dx); from 0 to 1 V=1.466 units^3 [/color] (correct answer: 1.571units^3) 
February 15th, 2011, 12:05 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Please Help......Volume Disk
1. You can't just switch x and y, this results in expressions that are not equivalent to the original, you need to solve for y: for nonnegative x Equating these two expressions for y will determine the limits of integration: thus x=0,4 Now, observing on (0,4) we have, using the washer method: 2. Here the thickness of each disk is dy and the radius is 9  x = 9  y² and at x = 9, y = 3 giving: 3. Here, we have the thickness of each washer is dx, the outer radius is and the inner radius is and we integrate from x = 0 to x = 1. 
February 20th, 2011, 07:11 PM  #3 
Newbie Joined: Feb 2011 Posts: 2 Thanks: 0  Re: Please Help......Volume Disk
I finially understand washer's method, thx a lot :P You explained the problems than my teacher, lol. 

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