Results 1 to 2 of 2

Math Help - cross-sections help please

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    36
    Awards
    1

    cross-sections help please

    consider A, if A is the area bounded by y=x^2 and y=1. Suppose a solid has a base A nd the cros sections of the solid perpendicular to the yaxis are equilateral triangles. sketch solid nd find volume.

    I know how to go about finding the area of A by evaluating the integral and I understand the concept of finding vol. by using cross sections but I dont know how to approach or start this problem. Can someone help please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, coe236!

    A is the area bounded by: . y\:=\:x^2\text{ and }y\:=\:1
    Suppose a solid has a base A and the cross-sections of the solid
    perpendicular to the y-axis are equilateral triangles.
    Sketch solid and find volume.

    The base looks like this:
    Code:
                    |
                   1|
           *--------+--------*
                    |
                x   |   x
            * - - - + - - - *
             *      |      *
               *    |    *
          - - - - - * - - - - - - 
                    |

    The area of an equilateral triangle with side s is: . A \:=\:\frac{\sqrt{3}}{4}s^2

    The side of our equilateral triangle is: . 2x

    Hence, the area of the triangle is: . A \:=\:\frac{\sqrt{3}}{4}(2x)^2 \:=\:\sqrt{3}\,x^2

    Since y \,=\,x^2, we have: . A \:=\:\sqrt{3}\,y


    Therefore, the volume is: . V \;=\;\sqrt{3}\int^1_0 y\,dy

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Volumes by Cross-Sections
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 31st 2010, 03:23 PM
  2. cross sections
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 21st 2009, 12:06 PM
  3. circular cross sections
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 10th 2009, 02:46 AM
  4. Cross sections of a region
    Posted in the Calculus Forum
    Replies: 4
    Last Post: October 2nd 2008, 08:28 PM
  5. Volume By Cross-Sections Help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 6th 2008, 03:50 PM

Search Tags


/mathhelpforum @mathhelpforum