# Thread: Volume of a solid given 5 planes

1. ## Volume of a solid given 5 planes

I know that the volume of a pyramid is:
1/3 * (area of base) * height

And I've found the area of a tetrahedron before,

But I have no idea how to find the area of a solid figure given five planes in the 3-D coordinate system.

The planes given are:
x + 2y - 2z = 2
2x + y + 2z = 4
x = 2
x = 0
z = 2

Any help or push in the right direction would be greatly appreciated

2. Originally Posted by jsmith90210
I know that the volume of a pyramid is:
1/3 * (area of base) * height

And I've found the area of a tetrahedron before,

But I have no idea how to find the area of a solid figure given five planes in the 3-D coordinate system.

The planes given are:
x + 2y - 2z = 2
2x + y + 2z = 4
x = 2
x = 0
z = 2

Any help or push in the right direction would be greatly appreciated
Start by drawing a picture. Since I have trouble drawing in 3 dimensions, I would start with just the xy-plane. x= 0 and x= 2 form the left and right boundaries. z= 2 is, of course, the "top".

x+ 2y- 2z= 2 and 2x+ y+ 2z= 4, at z= 2, give x+ 2y- 4= 2 or x+ 2y= 6 and 2x+ y+ 4= 4 or 2x+ y= 0. Draw those line also in `the xy-plane to see where they intersect the lines x= 0 and x= 2.
The planes x+ 2y- 2x= 2 and 2x+ y+ 2z= 4 intersect along the line 3x+ 3y= 6 or x+ y= 3.