Volume generated

  • Thread starter semc
  • Start date
  • #1
354
2
Volume generated[Solved]

Use polar coordinates to find the volume of the given solid enclosed by the hyperboloid -x2-y2+z2=1 and the plane z=2.

I wrote out the integral [tex]\int\int 1+r^2 dr d\vartheta[/tex] integrated from 0 to [tex]2\pi[/tex] and r integrated from 0 to sqrt3 and volume enclosed gotten to be [tex]15\pi[/tex]/2. So this is the volume enclosed by the hyperboloid and the xy-plane correct? So I wanted to use the volume of the cyclinder to subtract off the volume found previously. But the volume is [tex]6\pi[/tex] so if I subtract i would get negative volume?
 
Last edited:

Answers and Replies

  • #2
jav
35
0


Use polar coordinates to find the volume of the given solid enclosed by the hyperboloid -x2-y2+z2=1 and the plane z=2.

I wrote out the integral [tex]\int\int 1+r^2 dr d\vartheta[/tex] integrated from 0 to [tex]2\pi[/tex] and r integrated from 0 to sqrt3 and volume enclosed gotten to be [tex]15\pi[/tex]/2. So this is the volume enclosed by the hyperboloid and the xy-plane correct? So I wanted to use the volume of the cyclinder to subtract off the volume found previously. But the volume is [tex]6\pi[/tex] so if I subtract i would get negative volume?

It looks like you are integrating z^2 instead of z. Also shouldn't there be an extra r in the integral?

ie. [tex]\int\int z*r dr d\vartheta[/tex] whereas it looks like you are doing [tex]\int\int z^2 dr d\vartheta[/tex]
 

Related Threads on Volume generated

  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
4
Views
1K
Replies
1
Views
3K
  • Last Post
Replies
7
Views
2K
Replies
8
Views
544
Replies
1
Views
1K
Replies
1
Views
10K
Top