Let the region R be the area enclosed by the function f(x) = 2x and g(x) = 3x. If the region R is the base

Let the region R be the area enclosed by the function f(x) = 2x³ and g(x) = 3x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is a semi-circle with diameters extending through the region R, find the volume of the solid.