Notices
Results 1 to 9 of 9

Thread: volume of a triangular wedge

  1. #1 volume of a triangular wedge 
    ray
    ray is offline
    Suspended
    Join Date
    Sep 2011
    Posts
    82
    suppose we have a triangular prism ABC DEF[=A'B'C'], base: isosceles rectangle ABC [angle 90 at B]of side a=a and height h : volume is a*h / 2
    suppose now we cut it with a plane passing through B and DF , do you know the formula to calculate the volume of the [one of the] two solids?
    Thanks


    Last edited by ray; October 18th, 2011 at 10:31 AM.
    Reply With Quote  
     

  2.  
     

  3. #2  
    Suspended
    Join Date
    Apr 2007
    Location
    Pennsylvania
    Posts
    8,795
    Is this homework?


    Reply With Quote  
     

  4. #3  
    ray
    ray is offline
    Suspended
    Join Date
    Sep 2011
    Posts
    82
    I wish it were, Harold, my grandson left school!, a link will do.
    Last edited by ray; October 19th, 2011 at 03:03 AM.
    Reply With Quote  
     

  5. #4  
    Suspended
    Join Date
    Apr 2007
    Location
    Pennsylvania
    Posts
    8,795
    If I have pictured it correctly, one of the shapes is a pyramid with triangular base DEF and height h. Base DEF is the same as ABC, that is, it is a right triangle with two equal sides of length a. The area of the base is a / 2.
    Pyramid (geometry) - Wikipedia, the free encyclopedia says the volume of a pyramid is Bh/3 where B is the area of the base and h is the height from the base to the apex.
    This gives us V=a h/ 6.
    Reply With Quote  
     

  6. #5  
    ray
    ray is offline
    Suspended
    Join Date
    Sep 2011
    Posts
    82
    let's start with the cuboid ABCD, A'B'C'D', with square base a, V=ah, we cut it diagonally and we get a triangular prism with triangular base ABC : V= ah/2, now we cut it in two pieces with a plane passing trough B' and AC, the volume of this pyramid-wedge is one third and the other pyramid-pyramid with base AA'BB' 2/3 V =ah/3. Is that right?, so the cuboid V divides into 3 pyramid-parts, one of these is divided into two wedges. thanks Harold
    Reply With Quote  
     

  7. #6  
    Suspended
    Join Date
    Apr 2007
    Location
    Pennsylvania
    Posts
    8,795
    The area of the other piece of the prism is a h/ 2- a h/ 6 = a h/ 3, so I agree. What is the point of all this, Ray?
    Reply With Quote  
     

  8. #7  
    ray
    ray is offline
    Suspended
    Join Date
    Sep 2011
    Posts
    82
    don't be suspicious again, I thought Volume of a pyramid is different when vertex is not central
    Reply With Quote  
     

  9. #8  
    Suspended
    Join Date
    Apr 2007
    Location
    Pennsylvania
    Posts
    8,795
    I'm not suspicious, Ray. Just wondering why you posted this geometry problem.
    Reply With Quote  
     

  10. #9  
    ray
    ray is offline
    Suspended
    Join Date
    Sep 2011
    Posts
    82
    Quote Originally Posted by ray View Post
    , I thought Volume of a pyramid is different when vertex is not central
    just so, sorry if I disturbed you
    Reply With Quote  
     

Similar Threads

  1. Volume
    By Geo in forum Mathematics
    Replies: 5
    Last Post: June 21st, 2011, 01:23 PM
  2. volume of gases
    By STEPHANkIM5 in forum Chemistry
    Replies: 2
    Last Post: May 23rd, 2009, 09:48 AM
  3. max volume of a box
    By AlexP in forum Mathematics
    Replies: 13
    Last Post: October 20th, 2008, 07:55 AM
  4. Volume problem
    By 11rdc11 in forum Mathematics
    Replies: 18
    Last Post: August 3rd, 2008, 09:25 PM
  5. Parameterized volume
    By bit4bit in forum Mathematics
    Replies: 4
    Last Post: April 3rd, 2008, 07:39 PM
Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •