Volume of a region

  • Thread starter DWill
  • Start date
  • #1
70
0
Find the volume of this region: The tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1, 0, 0), (0, 2, 0), and (0, 0, 3).


Looking at this problem I thought it just involved solving a fairly simple triple integral:

||| dz dy dx

With these limits of integration:
0 <= x <= 1
0 <= y <= 2
0 <= z <= 3

I get the answer 6, but my textbook says the answer is 1. Is this a typo in the textbook or did I do something stupid?
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
What are the equations of the planes which make up the tetrahedron? What you have done appears to be calculating the volume of a cuboid in the first octant of dimensions 1x2x3. That's not the shape of a tetrahedron.
 
  • #3
70
0
Oh I see, I have to come up with the equations of the planes myself. that was stupid of me..thanks!
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,833
956
Using constants for limits of integration gives the volume of the rectangular solid 0 <= x <= 1, 0 <= y <= 2, 0 <= z <= 3.
 

Related Threads on Volume of a region

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
8
Views
2K
Replies
5
Views
11K
Replies
3
Views
25K
Replies
21
Views
2K
Replies
2
Views
7K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
Top