Volume of Cylinders with Triple Integrals

Cylindrical coordinates describe a point in three-dimensional space with three values: radial distance, angle, and height. The height gives the position above the xy-plane. The radial distance tells how far the point is from the z-axis, and the angle gives its direction from the positive x-axis in the xy-plane.

In a cylindrical coordinate system, a point P in three-dimensional space is described using the ordered triple r, theta, and z.

Here, z gives the height above the xy-plane, r represents the radial distance from the z-axis, and theta is the angle measured from the positive x-axis in the xy...