It is known that the area under the cycloid is three times the area of the circle that originated it, but ... does this relation remain for the volume under the revolution of the cycloid around its axis of symmetry and the volume of the sphere?

[math]f\left(t\right)=r\left(t-sin\left(t\right)-\pi\right)[/math][br][math]g\left(t\right)=r\left(1-cos\left(t\right)\right)[/math][br][br]Curve: [math]\left(f\left(t\right),0,g\left(t\right)\right)[/math] for [math]t\in\left[\pi,2\pi\right][/math][br][br]Surface: [math]\left(cos\left(s\right).f\left(t\right),sin\left(s\right).f\left(t\right),g\left(t\right)\right)[/math] for [math]t\in\left[\pi,2\pi\right][/math], [math]s\in\left[0,2\pi\right][/math][br][br]Volume: [math]2\pi r^3\left(\frac{3\pi^2}{4}-\frac{4}{3}\right)[/math] [br][br]Surface area: [math]8\pi r^2\left(\pi-\frac{4}{3}\right)[/math]