In a previous post we define the notion of general regions that allows us to calculate doubles integrals over these types of regions. This enables also to calculate the volume of a solid over these regions. Let's dive right into the solution of a problem.
Example
Solution
The solid is limited by the plane x = 0 or yz. the plane y = 0 or xz, the plane z = 0 or xy and the plane 2x +3y+z = 6. First we start by drawing the axes of coordinates then we draw part of the plane 2x+3y+z = 0. In order to do the latter, let's determine the coordinates intercepts.
Let's connect the points to form a triangle:
The triangle represents part of the plane 2x+3y+z = 6.. The plane intercepts the planes x = 0, y = 0, z = 0. This gives us the other faces of the tetrahedron, The base is limited by the x axis, the y axis and the line 2x + 3y = 6 as seen on the right.
Looking at the figure we see a solid with 4 triangular faces, It's called a tetrahedron or triangular pyramid. It consists of the three coordinates planes, the plane z = -2x-3y+6 with the bases limited by the lines y =o, x = 0 and the line 2x +3y = 6.
No comments:
Post a Comment