Funnel

The funnel surface is a regular surface and surface of revolution defined by the Cartesian equation

(1)

and the parametric equations

			(2)
			(3)
			(4)

for and . The coefficients of the first fundamental form are

			(5)
			(6)
			(7)

the coefficients of the second fundamental form are

			(8)
			(9)
			(10)

the area element is

(11)

and the Gaussian and mean curvatures are

			(12)
			(13)

The Gaussian curvature can be given implicitly as

(14)

Both the surface area and volume of the solid are infinite.