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3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex . A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that ...
Both a flat-faced cylinder and a cone are members of the power series. The power series nose shape is generated by rotating the y = R(x/L)n curve about the x -axis for values of n less than 1. The factor n controls the bluntness of the shape. For values of n above about 0.7, the tip is fairly sharp.
Frustum. In geometry, a frustum ( Latin for 'morsel'); [ a] ( pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone ...
The condition of balance ensures that the volume of the cone plus the volume of the sphere is equal to the volume of the cylinder. The volume of the cylinder is the cross section area, times the height, which is 2, or . Archimedes could also find the volume of the cone using the mechanical method, since, in modern terms, the integral involved ...
Intersection of a sphere and cone emanating from its center. A spherical sector (blue) A spherical sector. In geometry, a spherical sector, [ 1] also known as a spherical cone, [ 2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and ...
If one knows that the volume of a cone is (), then one can use Cavalieri's principle to derive the fact that the volume of a sphere is , where is the radius. That is done as follows: Consider a sphere of radius r {\displaystyle r} and a cylinder of radius r {\displaystyle r} and height r {\displaystyle r} .
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. If the plane passes through the center of the sphere (forming a great circle ), so that the height of the ...
Centroid. In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. [further explanation needed] The same definition extends to any object in - dimensional Euclidean space.