Results 1 to 4 of 4

Math Help - Volume of a soild...

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    33

    Angry Volume of a soild...

    Find the volume of the solid enclosed by the paraboloids and .

    I have no idea how to use integrals to solve this!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Aug 2008
    Posts
    903
    You have to draw the region first. See below. We're going from the brown which is the surface 25(x^2+y^2) to the blue which is 8-25(x^2+y^2). Since it's radially symmetrical, we can calculate just the volume over the first quadrant and then multiply by 4:

    V=4\int_0^{\sqrt{8/50}}\int_0^{\sqrt{8/50-x^2}}\int_{25(x^2+y^2)}^{8-25(x^2+y^2)} dzdydx

    May want to convert to spherical coordinates.
    Attached Thumbnails Attached Thumbnails Volume of a soild...-parab.jpg  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,693
    Thanks
    1466
    Quote Originally Posted by saxyliz View Post
    Find the volume of the solid enclosed by the paraboloids and .

    I have no idea how to use integrals to solve this!
    In cylindrical coordinates those are z= 25 r^2 and z= 8- 25 r^2. They intersect where 25r^2= 8- 25r^2 or [tex]50r^2= 8[tex] which has solution r= 2/5. The volume is given by
    \int_{\theta= 0}^{2\pi}\int_{r= 0}^{2/5} (8- 50 r^2)(r dr d\theta)
    Last edited by HallsofIvy; October 31st 2008 at 05:13 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2008
    Posts
    33
    Thank you so much to both of you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 18th 2011, 01:08 PM
  2. volume flux, mass flux and volume flo
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: June 7th 2011, 06:30 PM
  3. Replies: 1
    Last Post: May 14th 2010, 04:08 PM
  4. divergence = flux / volume is independant of the limiting volume
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: April 26th 2010, 07:31 PM
  5. Volume
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 9th 2008, 04:13 PM

Search Tags


/mathhelpforum @mathhelpforum