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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 r 2 + h 2 {\displaystyle {\sqrt {r^{2}+h^{2}}}} , where r {\displaystyle r} is the radius of the base and h {\displaystyle h} is the height.
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
If the directrix is a circle , and the apex is located on the circle's axis (the line that contains the center of and is perpendicular to its plane), one obtains the right circular conical surface or double cone. [2]
Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line.
A frustum's axis is that of the original cone or pyramid. A frustum is circular if it has circular bases; it is right if the axis is perpendicular to both bases, and oblique otherwise. The height of a frustum is the perpendicular distance between the planes of the two bases.
An example is a right circular cone. Circular symmetry in 3 dimensions has all pyramidal symmetry, C nv as subgroups. A double-cone, bicone, cylinder, toroid and spheroid have circular symmetry, and in addition have a bilateral symmetry perpendicular to the axis of system (or half cylindrical symmetry).
Right circular solid cone: r = the radius of the cone's base h = the distance is from base to the apex Solid sphere: r = the radius of the sphere ...