# Tetrahedron volume

• Nov 15th 2009, 08:09 PM
Tetrahedron volume
find volume of the tetrahedron bounded by the coordinate planes and the plane 2x+y+z=4

how do i begin to find the limits of integration? This always seems to be the hardest part of these type of problems.
• Nov 16th 2009, 03:20 AM
tonio
Quote:

find volume of the tetrahedron bounded by the coordinate planes and the plane 2x+y+z=4

how do i begin to find the limits of integration? This always seems to be the hardest part of these type of problems.

Intersection point with the z-axis: put x=y=0 and you get the point $(0,0,4)$, with the y-axis put x=z=0 and get $(0,4,0)$ and with the x-axis we get $(2,0,0)$.
Now you can use elementary geometry to calculate the volume $\frac{(area\,\,of\,\,basis)\cdot height}{3}$ , or triple intgration: anyway, the volume is $\frac{16}{3}$, if I didn't make a mistake somewhere.

Tonio
• Nov 16th 2009, 11:45 AM
so the limits of integration would be:

for z 0 to -8x-y+16

for y 0 to 4-2x

for z 0 to 2

I don't get the correct answer after using these limits