Spin a region around the x-axis. A thin rectangle sweeps out a disk.
A cross section at x has radius √x and area πx. Integrating these cross-sectional areas adds the disks into the solid. The displayed mesh is a sampled surface of revolution.
A disk’s area is πr², not its circumference 2πr.
Oblique view of the solid generated by y = √x around the x-axis. The highlighted ellipse is a circular cross section seen at an angle.