Find The Volume; Triple Integrals

  • #1
Find the volume of the solid enclosed by the paraboloids z = (x^2 + y^2 ) and z = 32 − ( x^2 + y^2) .


To make this problem easier to look at I resorting to making it into cylindrical coordinates.
{r, theta, z| 0< r< 1, 0<theta<2pi, r< z< 32-r}

Every time I solve for this I end up getting 31pi and I'm being told it's constantly wrong.
 
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Answers and Replies

  • #2
tiny-tim
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Welcome to PF!

Find the volume of the solid enclosed by the paraboloids z = (x^2 + y^2 ) and z = 32 − ( x^2 + y^2) .

0< r< 1

Hi withthemotive! Welcome to PF! :smile:

No, r goes from 0 to … ? :wink:

(but isn't it easier just to take horizontal slices of thickness dz, and just integrate once, over z?)
 
  • #3


Hi withthemotive! Welcome to PF! :smile:

No, r goes from 0 to … ? :wink:

(but isn't it easier just to take horizontal slices of thickness dz, and just integrate once, over z?)

LOL...oops.
I was looking at a similar problem on here, I think I might have figured it out now.
 

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