Visualising Solid Shapes | Study

Plane figures areof two-dimensions (2-D) and the solid shapes are of three- dimensions (3-D). The corners of a solid shape are called its vertices; theline segments ofits skeleton areits edges; and itsflat surfaces areits faces. A net is a skeleton-outline of a solid that can be folded to make it. The same solid can haveseveral types ofnets. Solid shapes can be drawn on a flat surface (like paper) realistically. We call this 2-D representation of a 3-Dsolid. Two types ofsketches of asolid are possible: (a) An oblique sketch does nothave proportional lengths. Still it conveys all important aspects of the appearance of the solid. (b) An isometric sketch is drawn on an isometric dot paper, a sample of which isgiven at theend of thisbook. In an isometric sketch of the solidthe measurements kept proportional. Visualising solidshapesis a veryuseful skill. Youshould be ableto see ‘hidden’ parts of thesolid shape. Different sections of a solid can be viewed in many ways: (a) One way is to viewby cutting or slicing the shape, whichwould result in the cross- section of thesolid. (b) Another way isby observing a 2-D shadow of a 3-Dshape. (c) A third wayis to lookat the shapefrom different angles; the front-view, theside- view and thetop view canprovide a lotof information aboutthe shape observed.

19. When a grouping symbol preceded by ‘ sign is removed or inserted, thenthe sign of eachterm of thecorresponding expression ischanged (from ‘ + ‘ to ‘−’ and from‘− ‘ to + ‘).