Finding the Volume of a Region Bounded by Two Planes in the First Octant

[Brad_Ad23]

It has been a long while since I've done any multiple integral stuff and I must say this question posed to me has me stumped, even though I suspect it is trivial.

1. Find the volume of the of the region bounded by the first octant and x+z=3 and y+5z=15


I figure since it is in the first octant of 3D Euclidean coordinate system the lower bound should involve at some point x,y,z = 0, and I think I also need to get the point of intersection of the two planes, which I came up with as y = 5x which I have no idea if it is helpful or not. So some guidance would be appreciated if possible!

 

[rootX]

Get the plane equation, and you would see that you are finding volume under that plane.

http://img77.imageshack.us/img77/1989/96274221xa5.png

 

[HallsofIvy]

The plane rootX is talking about is the one containing the lines x+ z= 3 with y=0, y+ 5z= 15 with x= 0, and 5x+ y= 15 with z= 0.