Right Circular Conoid

The right circular conoid is the right conoid having a circle as its directrix. A right circular conoid with base in the -plane, narrowing along the positive -axis, and with radius and height has parametric equations

			(1)
			(2)
			(3)

and Cartesian equation

(4)

The volume of the solid enclosed by capping the bottom is given by

			(5)
			(6)

The surface area (of the lateral portion only, thus excluding the base circle) is given by

(7)

This is more difficult to get in closed form, but for the case , the integral can be reduced to

			(8)
			(9)
			(10)

(OEIS A371923).