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# Conical Wedge

A conical wedge is an ungula obtained by cutting a solid cone with a plane placed at an angle oblique to its base.

For the special conical wedge obtained from a cone of height and base radius using a cutting plane through a diameter of the cone's base and inclined with respect to the base with slope , the volume, surface area, and wedge height can be obtained in closed form. In addition, the flat face lying in the cutting plane has the following shape for various values of and .

 condition top face shape ellipse parabola hyperbola

The height of a semicircular conical wedge is

 (1)

Define the integral

 (2) (3)

then the surface area of the curved side is

 (4)

and the volume is

 (5)

Plücker's conoid is sometimes also known as a cylindrical wedge.

Plücker's Conoid, Ungula

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## Cite this as:

Weisstein, Eric W. "Conical Wedge." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConicalWedge.html