Results 1 to 2 of 2

Math Help - Volume of 3-d shape

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    1

    Volume of 3-d shape

    The shape alone is for some reason hard for me to visualize and I also need to find the volume of the following shape called S

    The base of S is the triangular region on a graph with vertices (0,0), (1,0), and (0,1). Cross sections perpendicular to the y axis are equilateral triangles.

    The best thing I can come up with is some kid of skewed pyramid, and I'm clueless on the volume.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by slacker142 View Post
    The shape alone is for some reason hard for me to visualize and I also need to find the volume of the following shape called S

    The base of S is the triangular region on a graph with vertices (0,0), (1,0), and (0,1). Cross sections perpendicular to the y axis are equilateral triangles.

    The best thing I can come up with is some kid of skewed pyramid, and I'm clueless on the volume.
    Note what you are trying to do here. You are finding the volume of the solid via the method of slicing:

    First plot the triangular region. Once you do that, you can find the equation of the line that is created, connecting the points (0,1) and (1,0). I leave it for you to show that the line is y=1-x.

    Now, what do we do about each individual cross section?

    Recall that the area of a triangle is A=\tfrac{1}{2}bh

    The base here, is the distance from our line to the x axis: b(x)=1-x

    I leave it for you to show that the height of the equilateral triangle is \frac{\sqrt{3}}{2}b(x)=\frac{\sqrt{3}}{2}(1-x)

    So, A=\frac{\sqrt{3}}{4}(1-x)^2

    Thus, V=\frac{\sqrt{3}}{4}\int_0^1 (1-x)^2\,dx

    Can you try to make sense out of what I did?

    --Chris
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. What is the volume of this shape?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: December 4th 2010, 10:58 PM
  2. Volume of a Shape Under a Curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 25th 2010, 01:17 PM
  3. Replies: 3
    Last Post: March 30th 2009, 05:20 PM
  4. finding volume of a shape
    Posted in the Calculus Forum
    Replies: 6
    Last Post: September 25th 2008, 06:52 PM
  5. Volume of shape (NON CALC)
    Posted in the Geometry Forum
    Replies: 7
    Last Post: June 2nd 2007, 04:05 PM

Search Tags


/mathhelpforum @mathhelpforum