Q: what is cube, cuboid, cylinder and sphere

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Updated 4/13/2010 1:05:47 PM

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In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing incompatible definitions of a cuboid in the mathematical literature. In the more general definition of a cuboid, the only additional requirement is that these six faces each be a quadrilateral, and that the undirected graph formed by the vertices and edges of the polyhedron should be isomorphic to the graph of a cube.[1] Alternatively, the word “cuboid” is sometimes used to refer to a shape of this type in which each of the faces is a rectangle, and in which each pair of adjacent faces meets in a right angle; this more restrictive type of cuboid is also known as a right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.[2]

A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given straight line, the axis of the cylinder. The solid enclosed by this surface and by two planes perpendicular to the axis is also called a cylinder. The surface area and the volume of a cylinder have been known since deep antiquity.

In differential geometry, a cylinder is defined more broadly as any ruled surface spanned by a one-parameter family of parallel lines. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder.

A sphere (from Greek sfa??a—sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in three dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The maximum straight distance through the sphere is known as the diameter of the sphere. It passes through the center and is thus twice the radius.

In higher mathematics, a careful distinction is made between the sphere (a two-dimensional spherical surface embedded in three-dimensional Euclidean space) and the ball (the three-dimensional shape consisting of a sphere and its interior).