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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.
The lateral surface volume of a right spherical cone is = where is the radius of the spherical base and is the slant height of the cone (the distance between the 2D surface of the sphere and the apex).
English: This file illustrates a cone and its main caracteristics. Labeled "r" is the radius of the circular base. Labeled "h" is the height, from center of base to apex, of the cone. Labeled "c", is the slant height of the cone. Labeled "θ" is the angle between the height and the slant height.
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.
If the radius of the sphere is denoted by r and the height of the cap by h, the volume of the spherical sector is =. This may also be written as V = 2 π r 3 3 ( 1 − cos φ ) , {\displaystyle V={\frac {2\pi r^{3}}{3}}(1-\cos \varphi )\,,} where φ is half the cone angle, i.e., φ is the angle between the rim of the cap and the direction ...
More generally, when the directrix is an ellipse, or any conic section, and the apex is an arbitrary point not on the plane of , one obtains an elliptic cone [4] (also called a conical quadric or quadratic cone), [5] which is a special case of a quadric surface. [4] [5]
For a right circular cone, the surface area is = where = + is the slant height. Regular right symmetric n-gonal bipyramids: Bipyramid name Digonal bipyramid ...
That can also be rewritten as + [32] or (+) where r is the radius and l is the slant height of the cone. π r 2 {\displaystyle \pi r^{2}} is the base area while π r l {\displaystyle \pi rl} is the lateral surface area of the cone.