Find the volume of th eresulting solid by and method

  • Thread starter tony873004
  • Start date
  • #1
tony873004
Science Advisor
Gold Member
1,751
143
The region bounded by the curves is rotated about the specified axis. Find the volume of th eresulting solid by and method.

[tex]x^2 + \left( {y - 1} \right)^2 = 1[/tex]

First question want it rotated about the x-axis, the second question wants it rotated about the y-axis.

So I re-write it in terms of x. Seems easier than in terms of y since there's only 1 x term.
[tex]x = \sqrt { - y^2 + 2y}
[/tex]


The problem is when I graph it,
6_3_41b.GIF


So nothing is bounded. There is no solid to rotate. Should I have solved in terms of y instead? How would I do that?

Homework Statement





Homework Equations





The Attempt at a Solution

 
Last edited:

Answers and Replies

  • #2
cepheid
Staff Emeritus
Science Advisor
Gold Member
5,192
38
Don't you need to take both the positive and negative square roots?
 
  • #3
tony873004
Science Advisor
Gold Member
1,751
143
Don't you need to take both the positive and negative square roots?
Thanks for your reply.

It still seems like there is no bounded region. All the other problems in this section give a second curve, usually a line like y=2, just to bound the curve. What am I doing wrong? Did I properly solve for x?
6_3_41c.GIF
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
963
You have lost a "sign". x2+ (y-1)2= 1 is obviously a circle of radius 1 with center at (0, 1), not the hyperbola you show.

[tex]x= \pm \sqrt{1-(y-1)^2}= \pm \sqrt{2y- y^2}[/tex]
and
[tex]y= 1\pm \sqrt{1- x^2}[/tex]
 
  • #5
tony873004
Science Advisor
Gold Member
1,751
143
lol... and I should have recognized that the answer in the back of the book, 4pi/3 is the volume of a unit sphere. Without the r^3 in the formula I didn't recognize it.

Thanks, Halls
 

Related Threads on Find the volume of th eresulting solid by and method

Replies
1
Views
1K
Replies
1
Views
1K
Replies
1
Views
747
Replies
3
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
4
Views
3K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
11
Views
739
  • Last Post
Replies
9
Views
789
Top