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, , , ,     , • 3D shapes/objects are those which do not lie completely in a, plane., • 3D objects have different views from different positions., • A solid is a polyhedron if it is made up of only polygonal faces, the, faces meet at edges which are line segments and the edges meet at, a point called vertex., • Euler’s formula for any polyhedron is,, F+V–E=2, Where F stands for number of faces, V for number of vertices and, E for number of edges., • Types of polyhedrons:, (a) Convex polyhedron, A convex polyhedron is one in which all faces make it convex., e.g., , (1), , (2), , (3), , (4), , 12/04/18

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, (1) and (2) are convex polyhedrons whereas, (3) and (4) are non convex polyhedron., (b) Regular polyhedra or platonic solids:, A polyhedron is regular if its faces are congruent regular, polygons and the same number of faces meet at each vertex., For example, a cube is a platonic solid because all six of its, faces are congruent squares. There are five such solids–, tetrahedron, cube, octahedron, dodecahedron and icosahedron., e.g., , • A prism is a polyhedron whose bottom and top faces (known as, bases) are congruent polygons and faces known as lateral faces, are parallelograms (when the side faces are rectangles, the shape, is known as right prism)., • A pyramid is a polyhedron whose base is a polygon and lateral, faces are triangles., • A map depicts the location of a particular object/place in relation, to other objects/places., ,  , The front, top and side of a figure are shown. Use centimetre cubes to, build the figure. Then sketch the figure., 1., , 2., , Front, Top, Side, Front, Top, Side, 3. The views below represent a three-dimensional figure that cannot be, built from cubes. Determine which three-dimensional figures match, the views., A, , Front, , Top, , B, , C, , D, , Side, ,  , 12/04/18

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, • Scale is the relationship between the drawing’s/model’s, dimensions to the actual object’s dimensions., • In a map, symbols are used to depict the different objects and places., • Maps involve a scale which is fixed for a particular map., ,   , , , Explain how you would find the surface area of an open-top box that is, shaped like a rectangular prism., , , , Describe the shapes in a net used to cover a cylinder., ,   , In examples 1 and 2, write the correct answer from the given four, options., Example 1 : A prism is a polyhedron whose lateral faces are, , Solution, , (a) Circles, , (b) Triangles, , (c) Parallelograms, , (d) Rhombuses or Rhombi, , : Correct answer is (c)., , Example 2 : A pyramid is a polyhedron whose lateral faces are, , Solution, , (a) Rectangles, , (b) Triangles, , (c) Parallelograms, , (d) Rhombuses or Rhombi, , : Correct answer is (b)., , In examples 3 and 4, fill in the blanks to make the statements true, Example 3 : In a regular polyhedron ______ number, of faces meet at each vertex., Solution, , : same., , Example 4 : A pentagonal prism has ______ edges., Solution, , : 15., , In examples 5 and 6, state whether the statements are, true or false., Example 5 : A sphere is a polyhedron., Solution, , : False.,  , 12/04/18

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, Example 6 : In a prism the lateral faces need not be congruent, Solution, , : True., , Example 7 : Draw the top, front and side views of the given solid., , Solution, , :, , Front view, , Top view, , Side view, , , Use a compass and straight edge to create a larger version of each net, on a cardboard. Fold each net into a polyhedron., REGULAR POLYHEDRONS, NAME, , FACES, , Tetrahedron, , 4 triangles, , Octahedron, , 8 triangles, , Icosahedron, , 20 triangles, , Cube, , 6 squares, , Dodecahedron, , 12 pentagons, , EXAMPLE, , NET, ,  , 12/04/18

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, Example 8 : Use isometric dot paper to sketch a rectangular prism, with length 4 units, height 2 units and width 3 units., Solution, , : Steps:, (1) Draw a parallelogram, with sides 4 units and, 3 units., , Width, Length, , This is top of the prism, (Fig 1)., , Fig.1, , (2) Start at one vertex., Draw a line passing Height, through two dots., Repeat for other three, vertices. Draw the, hidden, edges as, dashed line (Fig 2)., , Fig. 2, , (3) Connect the ends of, the lines to complete, the prism (Fig 3)., , Fig. 3, ,  , 1. Complete the table for, the number of vertices, V, edges E and faces F, for, each, of, the, polyhedrons you made., 2. Make a Conjecture, What do you think is, true, about, the, relationship between, the number of vertices,, edges and faces of a, polyhedron?, , POLYHEDRON, , V, , E, , F, , V-E+F, , Tetrahedron, Octahedron, Icosahedron, Cube, Dodecahedron, ,  , 12/04/18

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, Example 9 : Identify the shape whose net is given below., , Solution, , : This shape is entirely made of equilateral triangles. When, folded, it results in a regular octahedron. Note that since, these are all equilateral and congruent faces, it is a, regular polyhedron., ,     , A polyhedron is formed by four or more polygons that intersect only at their, edges. The faces of a regular polyhedron are all congruent regular polygons, and the same number of faces intersect at each vertex, Regular polyhedrons, are also called Platonic solid. There are exactly five regular polyhedrons., , Example 10 : The solid given below is a rectangular prism or cuboid., Make all the diagonals of this shape., , Solution, , : There are only four diagonals as shown below., ,  , 12/04/18

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, Note that in a 3D shape, diagonals connect two vertices, that do not lie on the same face., E.g. the line segment from A to H in figure below is not, a diagonal for the solid. Diagonals must pass through, the inside of the shape. However, AH is diagonal of face, ADHE., , Example 11: Count the number of cubes in the given shapes., , Solution, , : (i) 8 cubes, , (ii) 6 cubes, , Example 12 : Name the following polyhedrons and verify the Euler’s, formula for each of them., , (a), Solution, , (b), , : S. No Polyhedron, , (c), , F, , V, , F+V, , E, , F + V –E, , (a), , Tetrahedron, , 4, , 4, , 8, , 6, , 2, , (b), (c), , Cube, Pentagonal, prism, , 6, 7, , 8, 10, , 14, 17, , 12, 15, , 2, 2, , Volume, the space inside a three-dimensional object, is measured in cubic, unit. If the blocks you build are each 1 cubic unit, then the volume of a, block structure is equal to the number of blocks in the structure. For example,, a structure made from eight blocks has a volume of 8 cubic units. If the, blocks have an edge length of 1 cm, the structure’s volume is 8 cm3., ,  , 12/04/18

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, Example 13 : A polyhedron has 7 faces and 10 vertices. How many, edges does the polyhedron have?, Solution, , : For any polyhedron,, F+V–E=2, Here, F = 7, V = 10, E = ?, Using above formula,, ⇒7 + 10 – E = 2, ⇒17 – E = 2, ⇒17 – 2 = E, ⇒ Ε = 15, , Example 14 : Find the number of vertices in a polyhedron which has, 30 edges and 12 faces., Solution, , : For any polyhedron,, F+V–E=2, Here, F = 12, V = ?, E = 30, Using above formula,, 12 + V – 30 = 2, V – 18 = 2, V = 2 + 18, V = 20, , Example 15 : The distance between City A and City B on a map is, given as 6 cm. If the scale represents 1 cm = 200 km,, then find the actual distance between City A and City B., Solution, , : Actual distance represented by 1cm = 200 km, ,   , What is the surface area of a single block in square units?, If the edge lengths of a block are 2 cm, what is the block’s surface area?, What is the volume of the structure at the right in cubic units?, What is the surface area of the structure above in square units?, (Remember: Count only the squares on the outside of the structure.), ,  , 12/04/18

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, Actual distance represented by 6 cm = 6 × 200 km, = 1200 km, So, actual distance between City A and City B is, 1200 km., Example 16 : Height of a building is 9 m and this building is represented, by 9 cm on a map. What is the scale used for the map?, Solution, , Size drawn, : Scale of map = Actual size, , 9 cm, 900 cm (because 9 m = 900 cm), 1, , 100, Thus, scale is 1:100., , , Example 17 : The scale on a map is 1 mm : 4 m. Find the distance on, the map for an actual distance of 52 m., Solution, , : Distance on map for an actual distance of 4 m = 1 mm, 1,  52, Distance on map for actual distance of 52 m , 4, = 13 mm, Thus, distance on map for actual distance of 52 m is, 13 mm., , All prisms have two identical, parallel faces. These two faces are always, polygons. A prism’s other faces are always parallelograms., A prism is sometimes referred to by the shape of the two identical faces on, its ends. For example, a triangular prism has triangular faces on its ends,, and a rectangular prism has rectangular faces on its ends., , Triangular Prism, , Rectangular Prism, , Example 18 : Application of problem, solving strategy, Determine the number of, edges, vertices and in the, following figure:,  , 12/04/18

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, Solution, , : Understand and Explore the problem, • What information is given in the question?, A cube with one of its corner cut., • What are you trying to find?, The no. of edges, vertices and faces., • Is there any information that is not needed?, The measures of edges are not needed., Plan a strategy, • Think of the definitions of an edge, vertex and faces, and try to co-relate them to the figure given above., Solve, • The polygonal regions are called faces, hence there are, 7 faces., • The line segment formed by the intersection of two faces, is called edges, hence there are 15 edges., • Edges meet at vertices which are points, hence there, are 10 vertices., Revise, • The above answer is verified using Euler’s Formula., F+V=E+2, For the above problem, F = 7, V = 10, E = 15, F + V = 7 + 10 = 17, E + 2 = 15 + 2 = 17, Hence F + V = E + 2 is verified., , These figures are prisms., , These figures are not prisms., ,  , 12/04/18

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,  , In each of the questions 1 to 21, out of four options only one is correct., Write the correct answer., 1. Which amongst the following is not a polyhedron?, , (a), , (b), , (c), , (d), , 2. Which of the following will not form a polyhedron?, (a) 3 triangles, , (b) 2 triangles and 3 parallelogram, , (c) 8 triangles, , (d) 1 pentagon and 5 triangles, , 3. Which of the following is a regular polyhedron?, (a) Cuboid, , (b) Triangular prism, , (c) Cube, , (d) Square prism, , 4. Which of the following is a two Dimensional figure?, (a) Rectangle, , (b) Rectangular Prism, , (c) Square Pyramid, , (d) Square Prism, , 5. Which of the following can be the base of a pyramid?, (a) Line segment, , (b) Circle, , (c) Octagon, , (d) Oval, , 6. Which of the following 3D shapes does not have a vertex?, (a) Pyramid, , (b), , Prism, , (c) Cone, , (d) Sphere, , 7. Solid having only line segments as its edges is a, (a) Polyhedron, , (b) Cone, , (c) Cylinder, , (d) Polygon, ,   , What do all the prisms have in common?, How are the non-prisms different from the prisms?, ,  , 12/04/18

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, 8. In a solid if F = V = 5, then the number of edges in this shape is, (a) 6, , (b), , 4, , (c) 8, , (d) 2, , 9. Which of the following is the top view of the given shape?, , (a), , (b), , (c), , (d), , 10. The net shown below can be folded into the shape of a cube. The, face marked with the letter L is opposite to the face marked with, which letter?, , (a) M, , (b) N, , (c) Q, , (d) O, , A net is a flat figure that can be folded to form a closed, three-dimensional, object. Such an object is called a solid., ,  , 12/04/18

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, 11. Which of the nets given below will generate a cone?, , (a), , (b), , (c), , (d), , 12. Which of the following is not a prism?, , (a), , (b), , (c), , (d), , 13. We have 4 congruent equilateral triangles. What do we need more to, make a pyramid?, (a) An equilateral triangle., (b) A square with same side length as of triangle., (c) 2 equilateral triangles with side length same as triangle., (d) 2 squares with side length same as triangle., ,   , 1. Explain how to find the surface area of a solid, from the net for that solid., 2. Here is a net for a rectangular solid. Take, whatever measurements you think are, necessary to find the solid’s volume and, surface area. Explain what measurements you, took and what you did with them., The surface area of a three-dimensional object is the space covering the, object’s surface. If you could pick up the object and flatten it so you could, see all sides at once, the area of the flat figure would be the surface area., (Don’t forget to count the bottom surface!) Surface area is also measured, in square units., ,  , 12/04/18

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, 14. Side of a square garden is 30 m. If the scale used to draw its picture, is 1cm: 5m, the perimeter of the square in the picture is, (a) 20 cm, , (b) 24 cm, , (c) 28 cm, , (d) 30 cm, , 15. Which of the following shapes has a vertex., , (a), (b), (c), (d), 16. In the given map, the distance between the places is shown using, the scale 1 cm : 0.5 km. Then the actual distance (in km) between, school and the book shop is, General, store, , Police, Station, , 4 cm, , 2 cm, School, 2.2 cm, Book, shop, , (a) 1.25, , (b) 2.5, , 5 cm, , 2 cm, Post, Office, , (c) 2, , (d) 1.1, ,  , To become familiar with some of the vocabulary terms in the chapter,, consider the following., 1. What does the term area total tell you about the meaning of surface, area?, 2. The word edge comes from the Latin word acer, meaning sharp. How, does the Latin root help you define an edge of a three-dimensional, figure?, 3. The word vertex can mean peak or highest point. What part of a cone, or pyramid is the vertex?, 4. The word prism comes from the Greek word priein, meaning to saw., How might you describe a prism in terms of something sawn or cut, off?, ,  , 12/04/18

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, 17. Which of the following cannot be true for a polyhedron?, (a) V = 4, F = 4, E = 6, , (b) V = 6, F = 8, E = 12, , (c) V = 20, F = 12, E = 30, , (d) V = 4, F = 6, E = 6, , 18. In a blueprint of a room, an architect has shown the height of the, room as 33 cm. If the actual height of the room is 330 cm, then the, scale used by her is, (a) 1:11, , (b), , 1:10, , (c) 1:100, , (d) 1:3, , 19. The following is the map of a town. Based on it answer question 19-21., , The number of hospitals in the town is, (a) 1, , (b), , 2, , (c) 3, , (d) 4, , There are two rectangular bases., There are four rectangular faces., The figure is a rectangular prism., There is one rectangular base., There are four triangular faces., The figure is a rectangular pyramid., There are two triangular bases., There are three rectangular faces., The figure is a triangular prism., There is one hexagonal base., There are six triangular faces., The figure is a hexagonal pyramid., ,  , 12/04/18

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, 20. The ratio of the number of general stores and that of the ground is, (a) 1 : 2, , (b) 2 : 1, , (c) 2 : 3, , (d) 3 : 2, , 21. According to the map, the number of schools in the town is, (a) 4, , (b) 3, , (c) 5, , (d) 2, , In questions 22 to 41, fill in the blanks to make the statements true., 22. Square prism is also called a _______., 23. Rectangular prism is also called a ________., , 24. In the figure,, , the number of faces meeting at B is ________., , 25. A pyramid on an n sided polygon has ______ faces., 26. If a solid shape has 12 faces and 20 vertices, then the number of, edges in this solid is ______., , 27. The given net, , can be folded to make a ______., , 28. A solid figure with only 1 vertex is a ______., 29. Total number of faces in a pyramid which has eight edges is______., 30. The net of a rectangular prism has ______ rectangles., (Hint: Every square is a rectangle but every rectangle is not a square.), Three-dimensional figures have three dimensions: length, width and, height. A flat surface of a three-dimensional figure is a face. An edge is, where two faces meet., A polyhedron is a three-dimensional figure whose faces are all polygons., A vertex of a polyhedron is a point where three or more edges meet. The, face that is used to name a polyhedron is called a base., ,  , 12/04/18

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, 31. In a three-dimensional shape, diagonal is a line segment that joins, two vertices that do not lie on the ______ face., 32. If 4 km on a map is represented by 1 cm, then 16 km is represented, by ______ cm., 33. If actual distance between two places A and B is 110 km and it is, represented on a map by 25 mm. Then the scale used is ______., 34. A pentagonal prism has ______ faces., 35. If a pyramid has a hexagonal base, then the number of vertices is, ______., , 36., , is the _______ view of, , 37. The number of cubes in, , are ______., , 38. If the sum of number of vertices and faces in a polyhedron is 14,, then the number of edges in that shape is ______., 39. Total number of regular polyhedra is ______., A prism has two bases, and a pyramid has one base., Prisms, , Pyramids, , A Prism is a polyhedron that has, two parallel, congruent bases. The, bases can be any polygon. The, other faces are parallelograms., , A pyramid is a polyhedron that, has one base. The base can be, any polygon. The other faces are, triangles., ,  , 12/04/18

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, 40. A regular polyhedron is a solid made up of ______ faces., 41. For each of the following solids, identify the front, side and top views, and write it in the space provided., (a), , (b), , The faces are all polygons, so the figure, is a polyhedron., There is one triangular base., The figure is a triangular pyramid., The faces are not all polygons, so the figure, is not a polyhedron., There are two circular bases., The figure is a cylinder., The faces are not all polygons, so the figure, is not a polyhedron., There is one circular base., The figure is a cone., ,  , 12/04/18

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, (c), , (d), , In each of the questions 42 to 61, state whether the following, statements are true (T) or false (F)., 42. The other name of cuboid is tetrahedron., 43. A polyhedron can have 3 faces., 44. A polyhedron with least number of faces is known as a triangular, pyramid., 45. Regular octahedron has 8 congruent faces which are isosceles, triangles., ,   , 1. Explain how to identify a prism or a pyramid., 2. Compare and contrast cylinders and prisms. How are they alike? How, are they different?, 3. Compare and contrast pyramids and cones. How are they alike? How, are they different?, ,  , 12/04/18

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, 46. Pentagonal prism has 5 pentagons., 47. Every cylinder has 2 opposite faces as congruent circles, so it is also, a prism., 48. Euler’s formula is true for all three-dimensional shapes., 49. A polyhedron can have 10 faces, 20 edges and 15 vertices., 50. The top view of, , is, , 51. The number of edges in a parallelogram is 4., 52. Every solid shape has a unique net., 53. Pyramids do not have a diagonal., 54. The given shape is a cylinder., , 55. A cuboid has atleast 4 diagonals., 56. All cubes are prisms., Cylinders and cones are not polyhedrons because they are not made of, faces that are all polygons., Cylinders, , Cones, , A cylinder has two parallel, A cone has one base that is a circle, congruent bases that are circles. and a surface that comes to a point, called the vertex., ,  , 12/04/18

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, 57. A cylinder is a 3-D shape having two circular faces of different radii., 58. On the basis of the given figure, the length of a rectangle in the net, of a cylinder is same as circumference of circles in its net., , 59. If a length of 100 m is represented on a map by 1 cm, then the, actual distance corresponding to 2 cm is 200 m., 60. The model of a ship shown is of height 3.5 cm. The actual height of, the ship is 210 cm if the scale chosen is 1: 60., , 61. The actual width of a store room is 280 cm. If the scale chosen to, make its drawing is 1:7, then the width of the room in the drawing, will be 40 cm., ,  , Find the volume of each prism., 1., , 2., , 3., ,  , 12/04/18

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, 62. Complete the table given below:, S., , Solid, , No, a., , Cuboid, , b., , Triangular, , Shape of, , Number, , Number, , Number, , Solid, , of faces F, , of Vertices V, , of edges E, , F+V, , E+2, , Pyramid, c., , Square, Pyramid, , d., , Rectangular, Pyramid, , e., , Pentagonal, Pyramid, , f., , Hexagonal, Pyramid, , g., , Triangular, Prism, , h., , Square, Prism, , i., , Cube, , j., , Pentagonal, Prism, , k., , Octagonal, Prism, , l., , Heptagonal, Prism, , 63. How many faces does each of the following solids, have?, (a) Tetrahedron, , (b) Hexahedron, , (c) Octagonal Pyramid, , (d) Octahedron, ,  , 12/04/18

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, 64. Draw a prism with its base as regular hexagon with one of its face, facing you. Now draw the top view, front view and side view of this, solid., 65. How many vertices does each of the following solids have?, (a) Cone, , (b) Cylinder, , (c) Sphere, , (d) Octagonal Pyramid, , (e) Tetrahedron, , (f), , Hexagonal Prism, , 66. How many edges does each of following solids have?, (a) Cone, , (b) Cylinder, , (c) Sphere, , (d) Octagonal Pyramid, , (e) Hexagonal Prism, , (f), , Kaleidoscope, ,       , The volume of a three-dimensional figure is the number of cubes it can, hold. One cube represents one cubic unit of volume., , 1. Use centimetre cubes to build the rectangular prism, shown. What are the length, width and height of the, prism? How many cubes does the prism hold?, 2. You can find out how many cubes the prism holds, without counting every cube. First look at the prism, from above. How can you find the number of cubes in, the top layer without counting every cube?, , Top, , 3. Now look at the prism from the side. How many layers, does the prism have? How can you use this to find the, total number of cubes in the prism?, Side, ,   , 1. Describe a shortcut for finding the number of cubes in a rectangular, prism., 2. Suppose you know the area of the base of a prism and the height of the, prism. How can you find the prism’s volume?, 3. Let the area of the base of a prism be B and the height of the prism be, h. Write a formula for the prism’s volume V., ,  , 12/04/18

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, 67. Look at the shapes given below and state which of these are polyhedra, using Euler’s formula., , (a), , (b), , (e), , (f), , (j), , (c), , (g), , (d), , (k), , (h), , (l), , (i), , (m), ,  , Find the volume of each cylinder., Use 3.14 for π and round to the nearest tenth., 1., , 2., , 3., ,  , 12/04/18

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, , , 1. Use a similar process to that in earlier Activity to develop, the formula for the volume of a cylinder. You will need an, empty can or other cylindrical pot. Remove one of the bases., 2. Arrange centimetre cubes in a single layer at the bottom of, the cylinder. Fit as many cubes into the layer as possible., How many cubes are in this layer?, 3. To find how many layers of cubes would fit in the cylinder,, make a stack of cubes along the inside of the cylinder., How many layers would fit in the cylinder?, 4. How can you use what you know to find the approximate, number of cubes that would fit in the cylinder?, , 68. Count the number of cubes in the given shapes., , (a), , (e), , (b), , (f), , (i), , (c), , (g), , (j), , (d), , (h), , (k), , (l),  , 12/04/18

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,   , 1. Suppose you know the area of the base of a cylinder and the height of, the cylinder. How can you find the cylinder’s volume?, 2. Let the area of the base of a cylinder be B and the height of the cylinder, be h. Write a formula for the cylinder’s volume V., 3. The base of a cylinder is a circle with radius r. How can you find the, area of the base? How can you use this in your formula for the volume, of a cylinder?, , 69. Draw the front, side and top view of the given shapes., , (a), , (g), , (b), , (c), , (h), , (d), , (i), , (e), , (f), , (j), ,  , 1. Use a net to construct a rectangular prism that is 3 cm by 6 cm by 9 cm., 2. Use a net to construct a cylinder with a height of 3 cm and a radius of, 1.5 cm (Hint: The length of the rectangle in the net must match the, circumference of the circles, so the length should be 2π r = 2π (1.5) ≈, 9.42 cm.), ,  , 12/04/18

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, , A net is a pattern of two-dimensions that can be folded to make a threedimensional figure. You can use 1 cm graph paper to help you make nets., , 1. Use a net to construct, rectangular prism., , a, , a. Draw the net at right on a piece, of graph paper. Each rectangle is, 10 squares by 4 squares. The two, squares are 4 small squares on, each side., b. Cut out the net. Fold the net along the edges, of each rectangle to make a rectangular prism., Tape the edges to hold them in place., 2. Use a net to construct a cylinder., a. Draw the net at right on a piece of graph, paper. The rectangle is 25 squares by 8, squares. Use a compass to make the circles., Each circle has a radius of 4 squares., b. Cut out the net. Fold the net as shown to, make a cylinder. Tape the edges to hold them, in place., , 70. Using Euler’s formula, find the value of unknown x, y, z, p, q, r, in, the following table., (i), , (ii), , (iii), , (iv), , (v), , (vi), , Faces, , 7, , y, , 9, , p, , 6, , 8, , Vertices, , 10, , 12, , z, , 6, , q, , 11, , Edges, , x, , 18, , 16, , 12, , 12, , r, ,   , 1. What are the dimensions, in inches, of the rectangular prism that you, built?, 2. What is the height, in cm, of the cylinder that you built? What is the, cylinder’s radius?, ,  , 12/04/18

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, 71. Can a polyhedron have V = F = 9 and E = 16 ? If yes, draw its figure., 72. Check whether a polyhedron can have V = 12, E = 6 and F = 8., 73. A polyhedron has 60 edges and 40 vertices. Find the number of its, faces., 74. Find the number of faces in the given shapes:, , 75. A polyhedron has 20 faces and 12 vertices. Find the edges of the, polyhedron., 76. A solid has forty faces and, sixty edges. Find the number of vertices, of the solid., 77. Draw the net of a regular hexahedron with side 3 cm. (Hint: Regular, hexahedron - cube), 78. Draw the net of a regular tetrahedron with side 6 cm., 79. Draw the net of the following cuboid:, ,   , 1. Tell whether a figure’s surface area has increased or decreased if each, dimension of the figure is changed by a factor of, , 1, ., 3, , 2. Explain how the surface area of a figure is changed if each dimension, is multiplied by a factor of 3., 3. Explain how the volume of a figure is changed if each dimension is, multiplied by a factor of 2., ,  , 12/04/18

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, 80. Match the following:, Figure, , Name, , (a), , (a) Hexahedron, , (b), , (b) Hexagonal Prism, , (c), , (c) Square Pyramid, , (d), , (d) Cone, , 81. Complete the table given below by putting tick mark across the, respective property found in the solids mentioned., Solids, Properties, , Cone, , Cylinder Prism Pyramid, , 1. The figure is a Polyhedron., 2. The figure has diagonals., 3. The shape has curved edges, 4. The base of figure is a polygon., 5. The bases are congruent, 6. The base of figure is a polygon, and other faces meet at a, single point., 7. The base of figure is a curved, edge and other faces meet at, a single point., 82. Draw the net of the following shape., ,  , 12/04/18

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, 83. Draw the net of the following solid., , (Hint: Pentagons are not congruent.), 84. Find the number of cubes in the base layer of the following figure., , 85. In the above figure, if only the shaded cubes are visible from the top,, draw the base layer., 86. How many faces, edges and vertices does a pyramid have with n, sided polygon as its base?, 87. Draw a figure that represents your mathematics textbook. What is, the name of this figure? Is it a prism?, 88. In the given figures, identify the different shapes involved., , 89. What figure is formed if only the height of a cube is increased or, decreased?, 90. Use isometric dot paper to draw each figure., (a) A tetrahedron., (b) A rectangular prism with length 4 units, width 2 units and height, 2 units.,  , 12/04/18

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, 91. Identify the nets given below and mention the name of the, corresponding solid in the space provided., Nets, , Name of Solid, , (a), , (b), , (c), , (d), , (e), , (f), ,  , 12/04/18

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, 92. Draw a map of your school playground. Mark all necessary places, like 2 library, Playground, Medical Room, Classrooms, Assembly, area, etc., 93. Refer to the given map to answer the following questions., , (a) What is the built-up area of Govt. Model School I ?, (b) Name the schools shown in the picture., (c) Which park is nearest to the dispensary?, (d) To which block does the main market belong?, (e) How many parks have been represented in the map?, 94. Look at the map given below., Answer the following questions., (a) Which two hospitals are opposite to each other?, (b) A person residing at Niti Bagh has to go to Chirag Delhi after, dropping her daughter at Asiad Tower. Mention the important, landmarks he will pass alongwith the roads taken., ,  , 12/04/18

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, (c) Name of which road is similar to the name of some month., B Town, India, Sector 26, 2, , 3, , 4, , 5, , 6, Police, Station, 8, , Fire, Station, 9, , 7, , 15, , Sector 27, , m, a, r, k, e, t, , Flower Road, , 1, , 20, , 17, , 18, , 14, , 19, , 13, Stadium, 16, , 12, , 1, 2, , Sneha Marg, , 11, , 3, 4, , Sector 20, , 2, , 1, , 16, , 15, , 14, , 10, , 11, , 12, , 9, , 8, , 7, , 3, , School, 13, , 5, , 6, 8, , College 7, , 10, , Mall Road, , 4, 5, , Sector 19, , 6, , g, ar, , 6, , Kh, , M, , 5, , el, , el, , 9, , Ma, , Kh, , rg, , Sports, Complex, , Nicolson Road, , Bank 1 (A), , 1, , 2, , 3, , 4, , 95. Look at the map given below., Houses, B Town, India, Sector 26, 2, , 3, , 4, , 5, , 6, Police, Station, 8, , Fire, Station, 9, , 7, , 15, , Sector 27, , m, a, r, k, e, t, , Flower Road, , 1, , 20, , 17, , 18, , 14, , 19, , 13, Stadium, 16, , 12, , 1, 2, , Sneha Marg, , 4, Sector 20, , 2, , 1, , 16, , 15, , 14, , 10, , 11, , 12, , 9, , 8, , 7, , 3, , School, 13, , 5, , 6, 8, , College 7, , 9, , 10, , Mall Road, , 4, 5, , Sector 19, , 6, , g, ar, , 6, , el, Kh, , M, , K, , Sports, Complex, , 5, , rg, Ma, , l, he, , Nicolson Road, , 11, , 3, , Bank 1 (A), , 1, , 2, , 3, , 4, ,  , 12/04/18

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, Now answer the following questions., (a) Name the roads that meet at round about., (b) What is the address of the stadium?, (c) On which road is the Police Station situated?, (d) If Ritika stays adjacent to bank and you have to send her a card,, what address will you write?, (e) Which sector has maximum number of houses?, (f) In which sector is Fire Station located?, (g) In the map, how many sectors have been shown?, 96. A photographer uses a computer program to enlarge a photograph., What is the scale according to which the width has enlarged?, , 97. The side of a square board is 50 cm. A student has to draw its image, in her notebook. If the drawing of the square board in the notebook, has perimeter of 40 cm, then by which scale the figure has been, drawn?, 98. The distance between school and house of a girl is given by 5 cm in, a picture, using the scale 1 cm : 5 km. Find the actual distance, between the two places?, ,  , 12/04/18

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, 99. Use a ruler to measure the distance in cm between the places joined, by dotted lines. If the map has been drawn using the scale 1 cm :10, km, find the actual distances between, (1) School and Library, (2) College and Complex, (3) House and School, , 100. The actual length of a painting was 2 m. What is its length in the, photograph if the scale used is 1 mm : 20 cm., , 101. Find the scale., (a) Actual size 12 m, Drawing size 3 cm, (b) Actual size 45 feet, Drawing size 5 inches, 102. In a town, an ice cream parlour has displayed an ice cream sculpture, of height 360 cm. The parlour claims that these ice creams and the, sculpture are in the scale 1:30. What is the height of the ice creams, served?,  , 12/04/18

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,  , Activity 1, , : Find the most appropriate way to reach from start to, finish., (Use a coloured pen of your choice to show the path, traced.), , Start, , Finish, , Start, Finish, ,  , 12/04/18

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, Activity 2, , Activity 3, , : Rohit is a 7 year old young boy. His uncle Raj asked him, to draw a map to reach Sport’s Complex from his (Rohit’s), house. He drew the following map., , Can you help Uncle Raj by drawing a better map, considering yourself as Rohit’s Father/Mother., : Look at the map of city given on the next page:, (a) Colour the map using the given colour code as follows., Blue-water, Red-Fire station, White-Hospital, GreenParks, Cream-River Bed, Brown-Mountains., (b) Mark the shortest route from House to Pool with the, help of arrowes., (c) Put X at the intersection of Chatra Marg and House, Lane., , Library, , House Lane, Sand, , Fire Station, Main Street, Park, , Health Lane, , Home, , Chatra Marg, , School, , Pool, Lake Street, Hospital, , River Lane, River, ,  , 12/04/18

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, Activity 4, , : Draw the nets given below on coloured sheets by taking, each side of the triangle as 3cm, and try to form the, shapes shown in front of it. Count the number of edges,, faces and vertices in ends and verify the Euler’s formula., , (a), , 4 equilateral triangles, , (b), , (c), , (d), 2 squares and 8 triangles, ,  , 12/04/18

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, , (e), , 2 pentagons and 10 triangles, , (f), 6 squares and 8 triangles, , (g), , Activity 5, , : Guess who am I? My name is given in the box below., Oops! Spelling of my name is jumbled up., Try to identify it from the clues given below and write it, in the blank space., (1) I am a polyhedron with least number of faces. ________, (2) I am a prism whose all faces are square. ________, (3) Looks like marbles but have no vertex. ________, (4) I am a solid whose base is polygonal and other faces, are triangles. ________, ,  , 12/04/18

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, , 6. Draw the map of your locality, showing the details of your sector/, block. Also highlight the appropriate landmarks which will help, your friend to locate your house in your sector/block., Activity 7 : Crossword Puzzle, Answer the following based on the hints given below., Across, 1., , Polyhedron whose lateral faces are parallelograms., , 2., , Prism having fifteen edges., , 5., , Another name for a square prism., , 7., , Polyhedron made up of four triangles., , 9., , Polyhedron made up of convex polygons., , Down, 2., , Polyhedron whose lateral faces are triangles., , 3., , In a solid shape, the line segment joining two vertices not lying, on the same face., , 4., , A 3-D shape having no vertex., , 6., , A solid figure having only one vertex., , 7., , Number of pentagons in a pentagonal prism., , 10. Point where edges of a solid shape meet., ,  , 12/04/18

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UNIT-6, , 3., , 2., , 4., , 1., , 6., , 10., , 5., 7., 8., , VISUALISING SOLID SHAPES, , 211, , 12/04/18

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MATHEMATICS, Rough Work, , 212, , EXEMPLAR PROBLEMS, , 12/04/18