The shaded region in the picture lies between the line $y = 2x$ and the parabola $y = x^2$. A potter turns it about the $x$-axis to make a solid with a hollow inside, with $x$ and $y$ in centimetres. What is the volume of the solid?

Fig. 1: A graph for x from 0 to 2.5. The straight line y = 2x and the parabola y = x squared both start at the origin and meet at the point (2, 4). The region between them is shaded light blue.