Page 1 VISUALISING SOLID SHAPES 277 277 277 277 277 15.1 INTRODUCTION: PLANE FIGURES AND SOLID SHAPES In this chapter, you will classify figures you have seen in terms of what is known as dimension. In our day to day life, we see several objects like books, balls, ice-cream cones etc., around us which have different shapes. One thing common about most of these objects is that they all have some length, breadth and height or depth. That is, they all occupy space and have three dimensions. Hence, they are called three dimensional shapes. Do you remember some of the three dimensional shapes (i.e., solid shapes) we have seen in earlier classes? Match the shape with the name: Chapter 15 Visualising Solid Shapes TRY THESE Fig 15.1 (i) (a) Cuboid (iv) (d) Sphere (ii) (b) Cylinder (v) (e) Pyramid (iii) (c) Cube (vi) (f) Cone Page 2 VISUALISING SOLID SHAPES 277 277 277 277 277 15.1 INTRODUCTION: PLANE FIGURES AND SOLID SHAPES In this chapter, you will classify figures you have seen in terms of what is known as dimension. In our day to day life, we see several objects like books, balls, ice-cream cones etc., around us which have different shapes. One thing common about most of these objects is that they all have some length, breadth and height or depth. That is, they all occupy space and have three dimensions. Hence, they are called three dimensional shapes. Do you remember some of the three dimensional shapes (i.e., solid shapes) we have seen in earlier classes? Match the shape with the name: Chapter 15 Visualising Solid Shapes TRY THESE Fig 15.1 (i) (a) Cuboid (iv) (d) Sphere (ii) (b) Cylinder (v) (e) Pyramid (iii) (c) Cube (vi) (f) Cone MATHEMATICS 278 278 278 278 278 Try to identify some objects shaped like each of these. By a similar argument, we can say figures drawn on paper which have only length and breadth are called two dimensional (i.e., plane) figures. We have also seen some two dimensional figures in the earlier classes. Match the 2 dimensional figures with the names (Fig 15.2): (i) (a) Circle (ii) (b) Rectangle (iii) (c) Square (iv) (d) Quadrilateral (v) (e) Triangle Fig 15.2 Note: We can write 2-D in short for 2-dimension and 3-D in short for 3-dimension. 15.2 FACES, EDGES AND VERTICES Do you remember the Faces, Vertices and Edges of solid shapes, which you studied earlier? Here you see them for a cube: (i) (ii) (iii) Fig 15.3 The 8 corners of the cube are its vertices. The 12 line segments that form the skeleton of the cube are its edges. The 6 flat square surfaces that are the skin of the cube are its faces. Page 3 VISUALISING SOLID SHAPES 277 277 277 277 277 15.1 INTRODUCTION: PLANE FIGURES AND SOLID SHAPES In this chapter, you will classify figures you have seen in terms of what is known as dimension. In our day to day life, we see several objects like books, balls, ice-cream cones etc., around us which have different shapes. One thing common about most of these objects is that they all have some length, breadth and height or depth. That is, they all occupy space and have three dimensions. Hence, they are called three dimensional shapes. Do you remember some of the three dimensional shapes (i.e., solid shapes) we have seen in earlier classes? Match the shape with the name: Chapter 15 Visualising Solid Shapes TRY THESE Fig 15.1 (i) (a) Cuboid (iv) (d) Sphere (ii) (b) Cylinder (v) (e) Pyramid (iii) (c) Cube (vi) (f) Cone MATHEMATICS 278 278 278 278 278 Try to identify some objects shaped like each of these. By a similar argument, we can say figures drawn on paper which have only length and breadth are called two dimensional (i.e., plane) figures. We have also seen some two dimensional figures in the earlier classes. Match the 2 dimensional figures with the names (Fig 15.2): (i) (a) Circle (ii) (b) Rectangle (iii) (c) Square (iv) (d) Quadrilateral (v) (e) Triangle Fig 15.2 Note: We can write 2-D in short for 2-dimension and 3-D in short for 3-dimension. 15.2 FACES, EDGES AND VERTICES Do you remember the Faces, Vertices and Edges of solid shapes, which you studied earlier? Here you see them for a cube: (i) (ii) (iii) Fig 15.3 The 8 corners of the cube are its vertices. The 12 line segments that form the skeleton of the cube are its edges. The 6 flat square surfaces that are the skin of the cube are its faces. VISUALISING SOLID SHAPES 279 279 279 279 279 Complete the following table: Table 15.1 Can you see that, the two dimensional figures can be identified as the faces of the three dimensional shapes? For example a cylinder has two faces which are circles, and a pyramid, shaped like this has triangles as its faces. We will now try to see how some of these 3-D shapes can be visualised on a 2-D surface, that is, on paper. In order to do this, we would like to get familiar with three dimensional objects closely . Let us try forming these objects by making what are called nets. 15.3 NETS FOR BUILDING 3-D SHAPES T ake a cardboard box. Cut the edges to lay the box flat. Y ou have now a net for that box. A net is a sort of skeleton-outline in 2-D [Fig154 (i)], which, when folded [Fig154 (ii)], results in a 3-D shape [Fig154 (iii)]. (i) (ii) (iii) Fig 15.4 DO THIS Vertex Face Edge Face Vertex Edge Faces (F) 64 Edges (E) 12 V ertices (V)84 Page 4 VISUALISING SOLID SHAPES 277 277 277 277 277 15.1 INTRODUCTION: PLANE FIGURES AND SOLID SHAPES In this chapter, you will classify figures you have seen in terms of what is known as dimension. In our day to day life, we see several objects like books, balls, ice-cream cones etc., around us which have different shapes. One thing common about most of these objects is that they all have some length, breadth and height or depth. That is, they all occupy space and have three dimensions. Hence, they are called three dimensional shapes. Do you remember some of the three dimensional shapes (i.e., solid shapes) we have seen in earlier classes? Match the shape with the name: Chapter 15 Visualising Solid Shapes TRY THESE Fig 15.1 (i) (a) Cuboid (iv) (d) Sphere (ii) (b) Cylinder (v) (e) Pyramid (iii) (c) Cube (vi) (f) Cone MATHEMATICS 278 278 278 278 278 Try to identify some objects shaped like each of these. By a similar argument, we can say figures drawn on paper which have only length and breadth are called two dimensional (i.e., plane) figures. We have also seen some two dimensional figures in the earlier classes. Match the 2 dimensional figures with the names (Fig 15.2): (i) (a) Circle (ii) (b) Rectangle (iii) (c) Square (iv) (d) Quadrilateral (v) (e) Triangle Fig 15.2 Note: We can write 2-D in short for 2-dimension and 3-D in short for 3-dimension. 15.2 FACES, EDGES AND VERTICES Do you remember the Faces, Vertices and Edges of solid shapes, which you studied earlier? Here you see them for a cube: (i) (ii) (iii) Fig 15.3 The 8 corners of the cube are its vertices. The 12 line segments that form the skeleton of the cube are its edges. The 6 flat square surfaces that are the skin of the cube are its faces. VISUALISING SOLID SHAPES 279 279 279 279 279 Complete the following table: Table 15.1 Can you see that, the two dimensional figures can be identified as the faces of the three dimensional shapes? For example a cylinder has two faces which are circles, and a pyramid, shaped like this has triangles as its faces. We will now try to see how some of these 3-D shapes can be visualised on a 2-D surface, that is, on paper. In order to do this, we would like to get familiar with three dimensional objects closely . Let us try forming these objects by making what are called nets. 15.3 NETS FOR BUILDING 3-D SHAPES T ake a cardboard box. Cut the edges to lay the box flat. Y ou have now a net for that box. A net is a sort of skeleton-outline in 2-D [Fig154 (i)], which, when folded [Fig154 (ii)], results in a 3-D shape [Fig154 (iii)]. (i) (ii) (iii) Fig 15.4 DO THIS Vertex Face Edge Face Vertex Edge Faces (F) 64 Edges (E) 12 V ertices (V)84 MATHEMATICS 280 280 280 280 280 Here you got a net by suitably separating the edges. Is the reverse process possible? Here is a net pattern for a box (Fig 15.5). Copy an enlarged version of the net and try to make the box by suitably folding and gluing together. (Y ou may use suitable units). The box is a solid. It is a 3-D object with the shape of a cuboid. Similarly, you can get a net for a cone by cutting a slit along its slant surface (Fig 15.6). You have different nets for different shapes. Copy enlarged versions of the nets given (Fig 15.7) and try to make the 3-D shapes indicated. (You may also like to prepare skeleton models using strips of cardboard fastened with paper clips). Fig 15.7 W e could also try to make a net for making a pyramid like the Great Pyramid in Giza (Egypt) (Fig 15.8). That pyramid has a square base and triangles on the four sides. See if you can make it with the given net (Fig 15.9). Fig 15.5 Fig 15.6 Cube (i) Cone (iii) Cylinder (ii) Fig 15.9 Fig 15.8 Page 5 VISUALISING SOLID SHAPES 277 277 277 277 277 15.1 INTRODUCTION: PLANE FIGURES AND SOLID SHAPES In this chapter, you will classify figures you have seen in terms of what is known as dimension. In our day to day life, we see several objects like books, balls, ice-cream cones etc., around us which have different shapes. One thing common about most of these objects is that they all have some length, breadth and height or depth. That is, they all occupy space and have three dimensions. Hence, they are called three dimensional shapes. Do you remember some of the three dimensional shapes (i.e., solid shapes) we have seen in earlier classes? Match the shape with the name: Chapter 15 Visualising Solid Shapes TRY THESE Fig 15.1 (i) (a) Cuboid (iv) (d) Sphere (ii) (b) Cylinder (v) (e) Pyramid (iii) (c) Cube (vi) (f) Cone MATHEMATICS 278 278 278 278 278 Try to identify some objects shaped like each of these. By a similar argument, we can say figures drawn on paper which have only length and breadth are called two dimensional (i.e., plane) figures. We have also seen some two dimensional figures in the earlier classes. Match the 2 dimensional figures with the names (Fig 15.2): (i) (a) Circle (ii) (b) Rectangle (iii) (c) Square (iv) (d) Quadrilateral (v) (e) Triangle Fig 15.2 Note: We can write 2-D in short for 2-dimension and 3-D in short for 3-dimension. 15.2 FACES, EDGES AND VERTICES Do you remember the Faces, Vertices and Edges of solid shapes, which you studied earlier? Here you see them for a cube: (i) (ii) (iii) Fig 15.3 The 8 corners of the cube are its vertices. The 12 line segments that form the skeleton of the cube are its edges. The 6 flat square surfaces that are the skin of the cube are its faces. VISUALISING SOLID SHAPES 279 279 279 279 279 Complete the following table: Table 15.1 Can you see that, the two dimensional figures can be identified as the faces of the three dimensional shapes? For example a cylinder has two faces which are circles, and a pyramid, shaped like this has triangles as its faces. We will now try to see how some of these 3-D shapes can be visualised on a 2-D surface, that is, on paper. In order to do this, we would like to get familiar with three dimensional objects closely . Let us try forming these objects by making what are called nets. 15.3 NETS FOR BUILDING 3-D SHAPES T ake a cardboard box. Cut the edges to lay the box flat. Y ou have now a net for that box. A net is a sort of skeleton-outline in 2-D [Fig154 (i)], which, when folded [Fig154 (ii)], results in a 3-D shape [Fig154 (iii)]. (i) (ii) (iii) Fig 15.4 DO THIS Vertex Face Edge Face Vertex Edge Faces (F) 64 Edges (E) 12 V ertices (V)84 MATHEMATICS 280 280 280 280 280 Here you got a net by suitably separating the edges. Is the reverse process possible? Here is a net pattern for a box (Fig 15.5). Copy an enlarged version of the net and try to make the box by suitably folding and gluing together. (Y ou may use suitable units). The box is a solid. It is a 3-D object with the shape of a cuboid. Similarly, you can get a net for a cone by cutting a slit along its slant surface (Fig 15.6). You have different nets for different shapes. Copy enlarged versions of the nets given (Fig 15.7) and try to make the 3-D shapes indicated. (You may also like to prepare skeleton models using strips of cardboard fastened with paper clips). Fig 15.7 W e could also try to make a net for making a pyramid like the Great Pyramid in Giza (Egypt) (Fig 15.8). That pyramid has a square base and triangles on the four sides. See if you can make it with the given net (Fig 15.9). Fig 15.5 Fig 15.6 Cube (i) Cone (iii) Cylinder (ii) Fig 15.9 Fig 15.8 VISUALISING SOLID SHAPES 281 281 281 281 281 Here you find four nets (Fig 15.10). There are two correct nets among them to make a tetrahedron. See if you can work out which nets will make a tetrahedron. Fig 15.10 EXERCISE 15.1 1. Identify the nets which can be used to make cubes (cut out copies of the nets and try it): (i) (ii) (iii) (iv) (v) (vi) 2. Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them. Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box. Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7. 3. Can this be a net for a die? Explain your answer . TRY THESE 1 2 3 4 5 6Read More

211 videos|109 docs|45 tests

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