joining the two. Right circular cone Volume For a circular cone with radius r and height h, the base is a circle of area and so the formula for volume becomes Slant height The slant height of a right circular cone is the distance from any point on the circle of its base to the apex via a line segment along the surface of the cone. It is given by , where is the radius of the base and is the height. This can be proved by the Pythagorean theorem. Surface area The lateral surface area of a right circular cone is where is the radius of the circle at the bottom of the cone and is the slant height of the cone. The surface area of the bottom circle of a cone is the same as for any circle, . Thus, the total surface area of a right circular cone can be expressed as each of the following: Radius and height (the area of the base plus the area of the lateral surface; the term is the slant height) where is the radius and is the height. Radius and slant height where is the radius and is the slant height. Circumference and slant height where is the circumference and is the slant height. Apex angle and height where is the apex angle and is the height. Circular sector The circular sector obtained by unfolding the surface of one nappe of the cone has: radius R arc length L central angle φ in radians Equation form The surface of a cone can be parameterized as where is the angle "around" the cone, and is the "height" along the cone. A right solid circular cone with height and aperture , whose axis is the coordinate axis and whose apex is the origin, is described parametrically as where range over , , and , respectively. In implicit form, the same solid is defined by the inequalities where More generally, a right circular cone with vertex at the origin, axis parallel to the vector , and aperture , is given by the implicit vector equation where or where , and denotes the dot product. Elliptic cone In the Cartesian coordinate system, an elliptic cone is the locus of an equation of the form It is an affine image of the right-circular unit cone with equation From the fact, that the affine image of