Grade7_Math_Book

VISUALISING SOLID SHAPES 289 Will it be same during (b) evenings? (a) forenoons? (ii) (iii) Fig 15.24 (i) - (iii) Study the shadows in relation to the position of the Sun and the time of observation. EXERCISE 15.4 1. A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions). © be reNpuCbEliRshTed to A ball not A cylindrical pipe A book (i) (ii) (iii) 2. Here are the shadows of some 3-D objects, when seen under the lamp of an overhead projector. Identify the solid(s) that match each shadow. (There may be multiple answers for these!) A circle A square A triangle A rectangle (i) (ii) (iii) (iv) 2020-21

290 MATHEMATICS 3. Examine if the following are true statements: (i) The cube can cast a shadow in the shape of a rectangle. (ii) The cube can cast a shadow in the shape of a hexagon. 15.5.3 A Third Way is by Looking at it from Certain Angles to Get Different Views One can look at an object standing in front of it or by the side of it or from above. Each time one will get a different view (Fig 15.25). Front view © Side view Top view be reNpuCbEliRshTed Fig 15.25 Here is an example of how one gets different views of a given building. (Fig 15.26) to not Front view Building Side view Top view Fig 15.26 You could do this for figures made by joining cubes. Fig 15.27 Try putting cubes together and then making such sketches from different sides. 2020-21

VISUALISING SOLID SHAPES 291 TRY THESE 1. For each solid, the three views (1), (2), (3) are given. Identify for each solid the corresponding top, front and side views. Solid Its views (1) (2) (3) © be reNpuCbEliRshTed to not 2. Draw a view of each solid as seen from the direction indicated by the arrow. (i) (ii) (iii) 2020-21

292 MATHEMATICS © WHAT HAVE WE DISCUSSED? be reNpuCbEliRshTed 1. The circle, the square, the rectangle, the quadrilateral and the triangle are examples to of plane figures; the cube, the cuboid, the sphere, the cylinder, the cone and the pyramid are examples of solid shapes. 2. Plane figures are of two-dimensions (2-D) and the solid shapes are of three-dimensions (3-D). 3. The corners of a solid shape are called its vertices; the line segments of its skeleton are its edges; and its flat surfaces are its faces. 4. A net is a skeleton-outline of a solid that can be folded to make it. The same solid can have several types of nets. 5. Solid shapes can be drawn on a flat surface (like paper) realistically. We call this 2-D representation of a 3-D solid. 6. Two types of sketches of a solid are possible: (a) An oblique sketchdoes not have 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 is given at the end of this book. In an isometric sketch of the solid the measurements kept proportional. 7. Visualising solid shapes is a very useful skill. You should be able to see ‘hidden’ parts of the solid shape. 8. Different sections of a solid can be viewed in many ways: (a) One way is to view by cutting or slicing the shape, which would result in the cross-section of the solid. (b) Another way is by observing a 2-D shadow of a 3-D shape. (c) A third way is to look at the shape from different angles; the front-view, the side-view and the top-view can provide a lot of information about the shape observed. not 2020-21