Find the volume of the solid right cylinder whose base is the region in the xy – plane that lies inside the cardioid r = 1 + cos θ and outside the circle r = 1 and whose top lies in the plane z = 4.

The cylinder's volume is the product of its height and the area of its base. We're told that the height is restricted to the plane , so the height is 4.

The area of the base is obtained by the integral,

Then the volume of the cylinder is 8 + π.

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: