Results 1 to 2 of 2

Math Help - Help on emptying a tank of oil

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    4

    Help on emptying a tank of oil

    A spherical tank of radius 8 feet is half full of oil that weighs 50 pounds per cubic foot.

    Find the work required to pump oil out through a hole in the top of the tank.

    Hints: Set the center of the sphere at (0,8) in a coordinate plane. Consider that a slice of the sphere is a circle.

    Graphs would be helpful.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Feb 2010
    Posts
    148
    Thanks
    2

    Thumbs down

    Quote Originally Posted by ifchickenhadlips View Post
    A spherical tank of radius 8 feet is half full of oil that weighs 50 pounds per cubic foot.

    Find the work required to pump oil out through a hole in the top of the tank.

    Hints: Set the center of the sphere at (0,8) in a coordinate plane. Consider that a slice of the sphere is a circle.

    Graphs would be helpful.
    W=F\cdot d

    F=50V
    where V is the approxmation of the volume of one slice of oil.

    I put the center of the sphere at (0, 0) so the radius of each slice is
    \sqrt{64-y^2}

    Then V=\pi(\sqrt{64-y^2})^2\,dy

    d=8-y

    So W=\int_{-8}^0\pi(64-y^2)(8-y)\,dy
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Emptying Tanks Modelling with Euler's Method
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 22nd 2009, 10:51 PM
  2. Work done emptying a cylindrical tank
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: October 3rd 2009, 02:59 AM
  3. Emptying a water tank (Inverted circular cone)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 20th 2009, 05:05 PM
  4. Replies: 1
    Last Post: December 4th 2007, 04:45 PM
  5. Emptying a tank
    Posted in the Algebra Forum
    Replies: 5
    Last Post: July 29th 2007, 06:32 AM

Search Tags


/mathhelpforum @mathhelpforum