1. The problem statement, all variables and given/known data Use polar coordinates to find the volume of the solid where T is the region that lies under the plane 3x+4y+z=12, above the xy-plane, and inside the cylinder x^2+y^2=2x. 2. Relevant equations None. 3. The attempt at a solution Here's my work: x^2+y^2=2x x^2-2x+y^2=0 x^2-2x+1+y^2=1 (x-1)^2+y^2=1 (r*cos(theta)-1)^2+(r*sin(theta))^2=1 r^2(cos(theta))^2-2r*cos(theta)+1+r^2(sin(theta))^2=1 r^2-2r*cos(theta)=0 factor r(r-2*cos(theta))=0 r-2cos(theta)=0 r=2cos(theta) V=r dz dr d(theta) from 0 to 2pi, from 0 to 2cos(theta), from 0 to 12-3r(cos(theta))-4r(sin(theta)) =18pi But the answer in the book is 9pi. Which answer is right?