A 6-inch-tall plastic cup is shaped like a surface obtained by rotating a line segment in the first quadrant about the x-axis. Given that the radius of the base of the cup is 1 inch, the radius of the...

A 6-inch-tall plastic cup is shaped like a surface obtained by rotating a line segment in the first quadrant about the x-axis. Given that the radius of the base of the cup is 1 inch, the radius of the top of the cup is 2 inches, and the cup is filled to the brim with water, use integration to approximate the volume of the water in the cup.