Results 1 to 2 of 2

Math Help - Volumes - Linear Relationships

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    29

    Exclamation Volumes - Linear Relationships

    Hi

    For this question:

    A symmetrical pier of height 5 m has an elliptical base with equation x^2/25 + y^2/4 = 1 and slopes to a parallel elliptical top with equation x^2/9 + y^2 = 1. If the cross sections of the area parallel to the base are also elliptical find the volume of the pier given that the area of an ellipse with semi-major axis a and semi-minor axis b is pi * a *b.

    How exactly do I find a and b in terms of h? I know I need to do something with linear relationships but I've forgotten the method. Is it something to do with y = ax+b?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Failure's Avatar
    Joined
    Jul 2009
    From
    Zürich
    Posts
    555
    Quote Originally Posted by UltraGirl View Post
    Hi

    For this question:

    A symmetrical pier of height 5 m has an elliptical base with equation x^2/25 + y^2/4 = 1 and slopes to a parallel elliptical top with equation x^2/9 + y^2 = 1. If the cross sections of the area parallel to the base are also elliptical find the volume of the pier given that the area of an ellipse with semi-major axis a and semi-minor axis b is pi * a *b.

    How exactly do I find a and b in terms of h? I know I need to do something with linear relationships but I've forgotten the method. Is it something to do with y = ax+b?
    Let a(z) be the major half-axis, b(z) the minor half-axis at hight z.
    You know that a(0)=5, b(0)=2 and a(h)=3, b(h)=1. Assuming that a(z), b(z) are linear functions of z, you get that
    a(z)=a(0)+\frac{a(h)-a(0)}{h}\cdot z and b(z)=b(0)+\frac{b(h)-b(0)}{h}\cdot z

    Now integrate the cross section A(z) := \pi a(z)\cdot b(z) from z=0 to z=h.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: February 11th 2010, 08:08 PM
  2. Asymmetric Relationships
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: February 5th 2010, 10:27 AM
  3. Questionnaire Relationships
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: April 12th 2009, 11:25 AM
  4. Relationships between Max and Min
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 31st 2008, 04:39 AM
  5. Linear vs. Proportional relationships
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 14th 2008, 05:34 AM

Search Tags


/mathhelpforum @mathhelpforum