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