Search results
Results From The WOW.Com Content Network
The "base radius" of a circular cone is the radius of its base; often this is simply called the radius of the cone. The aperture of a right circular cone is the maximum angle between two generatrix lines; if the generatrix makes an angle θ to the axis, the aperture is 2 θ .
This is a list of volume formulas of basic shapes: [4]: 405–406 Cone – 1 3 π r 2 h {\textstyle {\frac {1}{3}}\pi r^{2}h} , where r {\textstyle r} is the base 's radius Cube – a 3 {\textstyle a^{3}} , where a {\textstyle a} is the side's length;
The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P. The cone over a disk is the solid cone of classical geometry (hence the concept's name). The cone over a circle given by
This is analogous to the way a plane angle projected onto a circle defines a circular arc on the circumference, whose length is proportional to the angle. Steradians can be used to measure a solid angle of any shape. The solid angle subtended is the same as that of a cone with the same projected area.
An example of a spherical cap in blue (and another in red) In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.It is also a spherical segment of one base, i.e., bounded by a single plane.
The value 75.4 = 24 π, where 24 π substitutes for factor of 12 π in the formula for a volume of frustum of a cone encompassing a full tree using one base circumference, converting it to a volume formula that uses a basal circumference that is the average of circumferences C 1 and C 2.
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]
In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X , the relative Spec C = Spec X R {\displaystyle C=\operatorname {Spec} _{X}R}