Using polar coordinates to find the volume of a bounded solid

  • Thread starter paraboloid
  • Start date
  • #1
17
0
Using polar coordinates to find the volume of a bounded solid[Solved]

zoiy4o.png

I found the equation of the boundary circle by setting z to 4 in the paraboloid.
Then I did some work to get polar coords:
[tex]x^2+y^2 = 1[/tex]
[tex]x^2+y^2 = r^2[/tex]
[tex]1-x^2-y^2 = 1-r^2[/tex]
Then I set up my integral as such
[tex]\int_0^{2\pi}\int_{0}^{1}(1-r^2)rdrd\theta[/tex]
After the double integration, I get pi/2.

edit: It should be 4r-4r3 as the integrand.
 
Last edited:

Answers and Replies

  • #2
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,883
1,461
Why are you plugging 1-r2 in as the integrand? What are zupper and zlower?
 
  • #4
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,883
1,461
Draw a sketch of the volume you're integrating. It'll help you visualize what goes where.
 

Related Threads on Using polar coordinates to find the volume of a bounded solid

Replies
5
Views
7K
Replies
2
Views
2K
Replies
11
Views
23K
Replies
2
Views
3K
Replies
1
Views
1K
Replies
2
Views
629
Replies
7
Views
874
  • Last Post
Replies
1
Views
14K
Top