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   Cone Formulas   

also see Defining Geometric Figures  Cone    A cone is a surface generated by a family of all lines through a given point (the vertex)    and passing through a curve in a plane (the directrix). More commonly, a cone includes    the solid enclosed by a cone and the plane of the directrix. The region of the plane    enclosed by the directrix is called a base of the cone. The perpendicular distance from    the vertex to the plane of the base is the height of the cone.     Height: h Area of base: B Volume: V     V = hB/3   Circular Cone     A cone whose base is a circle. The line connecting the center of the base to the vertex is called the axis of the circular cone.  Right Circular Cone      In a right circular cone, the axis is perpendicular to the base. (If the axis of a      circular cone is not perpendicular to the base, it is called an oblique circular cone.)      The length of any line segment connecting the vertex to the directrix is called the      slant height of the cone.      Height: h      Radius of base: r      Slant height: s      Lateral surface area: S      Total surface area: T      Volume: V           B = Pi r2           s = sqrt[r2+h2]           S = Pi rs           T = Pi r(r+s)           V = Pi r2h/3   (Learn how to build a cone from paper or other flat material.)  Frustum of a Right Circular Cone      The part of a right circular cone between the base and a plane parallel to the base      whose distance from the base is less than the height of the cone.        Height: h      Radius of bases: r, R      Slant height: s      Lateral surface area: S      Total surface area: T      Volume: V           s = sqrt([R-r]2+h2)           S = Pi(r+R)s           T = Pi(r[r+s]+R[R+s])           V = Pi(R2+rR+r2)h/3     (Learn how to build a frustum from paper or other flat material.)   For more about cones, visit: Ask Dr. Math: Lateral Surface of a Cone Volume of a Cone Volume of a Cone Volume and Surface Area of a Cone Frustum The Geometry Center: Cones Back to Contents

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