Let $V = \{(x, y, z): x^2 + y^2 ≤ 4$ and $0 \le z \le 4\}$ be a cylinder and let $P$ be the plane through $(4, 0, 2)$, $(0, 4, 2)$ and $(−4, −4, 4)$. Compute the volume of $C$ below the plane $P$.
I have absolutely no idea how to start this question. I was thinking using Cavalieri’s Principle but I'm not quite sure how to or if there's another way of working it out. Please help.
the normal of the plane is given by taking the cross product of the first point minus the second times the first point times the third. It is i+j+6k. Then the equation of the plane is given by equating the dot product of the normal times the diference between (x,y,z) and the first point with 0. Is is z=(16-x-y)/6=(i6-rcosa-rcosa)/16. Now the volume is given by taking the double integral in polar coordinates over the region 0<=r<=1 and 0<=a<=2.pi of (i6-rcosa-rcosa)/16.