In physics and mathematics, the dimension of a space or object is informally defined as the
minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because
only one coordinate is needed to specify a point on it. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two
because two coordinates are needed to specify a point on it (for example, to
locate a point on the surface of a sphere you need both its latitude and its longitude). The inside of a cube, a cylinder or a sphere is
three-dimensional because three co-ordinates are needed to locate a point
within these spaces.
http://en.wikipedia.org/wiki/Dimension
Cross section (geometry)
In geometry, a cross-section is the intersection of a figure in 2-dimensional
space with a line, or of a body in 3-dimensional space with a plane, etc. More
plainly, when cutting an object into slices one gets many parallel cross-sections. (Our solved example in mathguru.com uses this concept)
http://en.wikipedia.org/wiki/Cross_section_(geometry)
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