3. [AS5] Identify the net of a cylinder. (A) (B) (C) (D) EXERCISE 14.2. NETS OF 3–D SHAPES 49
4. [AS5] Identify the net of a triangular pyramid. (A) (B) (C) (D) EXERCISE 14.2. NETS OF 3–D SHAPES 50
5. [AS5] Identify the net of a cuboid. [] (A) 51 (B) (C) (D) Very Short Answer Type Questions 6 [AS1] State true or false. (i) Flat surfaces of solid shapes are called their edges. EXERCISE 14.2. NETS OF 3–D SHAPES
[AS1] Fill in the blanks. (ii) A net of the cube is _____. (iii) A cube has diagonals. [AS1] Answer the following questions in one sentence. (iv) Define the net of a solid. (v) Make a net of the given cylinder. 7 [AS1] Answer the following questions in one sentence. (i) What do you mean by visualising solid shapes? EXERCISE 14.2. NETS OF 3–D SHAPES 52
8 [AS2] Answer the following questions in one sentence. (i) Match the nets with the shapes. (ii) Three nets for the shape are given here. Match the net with its 3D–shape. (iii) Identify the nets which can be used to make cubes. EXERCISE 14.2. NETS OF 3–D SHAPES 53
(iv) Three nets for the shape are given here. Match the net with its 3-D shape. EXERCISE 14.2. NETS OF 3–D SHAPES 54
EXERCISE 14.3 DRAWING SOLIDS ON A FLAT SURFACE 14.3.1 Key Concepts i. Oblique sketches are drawn on a grid paper to visualize 3 - D shapes. ii. Isometric sketches can be drawn on a dot isometric paper to visualize 3 -D shapes. 14.3.2 Additional Questions Objective Questions 1. [AS3] A sketch intended to depict a perspective of an item in three dimensions is called . (A) An oblique sketch (B) A direct sketch (C)An actual sketch (D)None of these 2. [AS3] In an oblique sketch, the sizes of the front face and its opposite face are . (A) Not equal (B) Equal (C) Perpendicular (D)None of these 3. [AS3] To draw sketches in which measurements agree with those of the given solid we use . (A) A graph paper (B) An isometric dot sheets (C) A protractor (D) Set squares 4. [AS3] A/an sketch does not have proportional lengths. (A) Isometric (B) Oblique (C) Actual (D) Virtual EXERCISE 14.3. DRAWING SOLIDS ON A FLAT SURFACE 55
5. [AS3] A/an sketch is drawn on an isometric dot paper. (A) Oblique (B) Isometric (C) Virtual (D) Actual Very Short Answer Type Questions 6 [AS3] Answer the following questions in one sentence. (i) What is an oblique sketch? (ii) What is an isometric sketch? 7 [AS5] Answer the following questions in one sentence. (i) Draw an isometric sketch of a cuboid of dimensions 3 × 2 × 2. (ii) Draw an isometric sketch of a cuboid of dimensions 5 × 3 × 2. (iii) Three cubes each with 4 cm edge are placed side by side to form a cuboid. Draw an oblique sketch of this cuboid. Short Answer Type Questions 8(i) [AS5] Draw an oblique isometric sketch of a cuboid of dimensions 4 × 3 × 2. (ii) [AS5] Make an oblique sketch for each of the given isometric sketches. EXERCISE 14.3. DRAWING SOLIDS ON A FLAT SURFACE 56
EXERCISE 14.4 VISUALISING SOLID OBJECTS 14.4.1 Key Concepts i. Sometimes when we look at combined shapes, some of them may be hidden from our view. In such cases, visualisations are very helpful. ii. Suppose we form a cuboid by joining cubes. We will be able to estimate the length, breadth and height of the cuboid. 14.4.2 Additional Questions Objective Questions 1. [AS3] The horizontal cross section of a cylinder is a . (A) Rectangle (B) Circle (C) Square (D) Parallelogram 2. [AS3] The vertical cross section of a cylinder is a . (A) Rectangle (B) Circle (C) Square (D) Parallelogram 3. [AS3] The horizontal cross section of a cone is a . (A) Rectangle (B) Circle (C) Square (D) Parallelogram 4. [AS3] The vertical cross section of a cone is a . (A) Rectangle (B) Circle (C) Square (D) Triangle EXERCISE 14.4. VISUALISING SOLID OBJECTS 57
5. [AS1] Three cubes of side 4 cm each are joined end to end. The breadth of the resulting cuboid is . (A) 12 cm (B) 8 cm (C)4 cm (D)10 cm Very Short Answer Type Questions 6 [AS5] Answer the following questions in one sentence. (i) Keep a torchlight, right in front of a cube as shown. What is the shape of the shadow obtained? Draw it. (ii) Keep a torchlight, right in front of a ball as shown. What is the shape of the shadow obtained? Draw it. (iii) Keep a torchlight, right in front of a cuboidal box. What is the shape of the shadow obtained? Draw it. EXERCISE 14.4. VISUALISING SOLID OBJECTS 58
(iv) A bulb is kept burning just above a cylindrical pipe. Name the shape of the shadow obtained and draw it. (v) Keep a torchlight, right in front of a cone as shown. Of what shape is the shadow obtained? Draw it. 7 [AS5] State true or false. (i) The shadow of a cone is a triangle. [] [AS5] Answer the following questions in one sentence. (ii) Here is the shadow of a 3D object, when seen under the lamp of an overhead projector. Identify the solid(s) that match this shadow. (iii) Here is the shadow of a 3D object, when seen under the lamp of an overhead projector. Identify the solid(s) that matches this shadow. EXERCISE 14.4. VISUALISING SOLID OBJECTS 59
(iv) Here is the shadow of a 3-D object, when seen under the lamp of an overhead projector. Identify the solid(s) that matches this shadow. (v) Here is the shadow of a 3D object, when seen under the lamp of an overhead projector. Identify the solid(s) that matches this shadow. Short Answer Type Questions 8(i) [AS1] If two cuboids of dimensions 3 cm × 3 cm × 6 cm are placed one above the other, what would the dimensions of the resulting solid be? (ii) [AS1] If two cubes of dimensions 4 cm by 4 cm by 4 cm are placed side by side, what would the dimensions of the resulting cuboid be? 9 [AS2] What are the cross-sections obtained when you give a (i) vertical cut (ii) horizontal cut to the following solids? a) An ice cube b) A circular pipe c) A joker’s cap 10 [AS2] What are the cross-sections obtained when you give a (i) vertical cut (ii) horizontal cut to the following solids? a) A brick b) A round apple EXERCISE 14.4. VISUALISING SOLID OBJECTS 60
CHAPTER 15 SYMMETRY EXERCISE 15.1 LINE SYMMETRY 15.1.1 Key Concepts i. Line of symmetry: The line which divides a figure into two identical parts is called the line of symmetry or axis of symmetry. Ex: In the given figure, the dotted lines are the lines of symmetry. ii. An object can have one or more than one lines of symmetry or axes of symmetry. Ex. In the given figure, there are two lines of symmetry. 15.1.2 Additional Questions Objective Questions 1. [AS3] The dotted line which divides a figure into two equal parts is the . (A) Axis of symmetry (B) Median (C) Altitude (D)Dividing line 2. [AS4] The number of lines of symmetry for the letter A is . (A) 1 (B) 2 (C) 3 (D) 4 EXERCISE 15.1. LINE SYMMETRY 61
3. [AS3] The number of lines of symmetry of a circle is . (A) 2 (B) 4 (C) 5 (D)Infinitely many 4. [AS4] The number of lines for symmetry of the letter K is . (A) 0 (B) 1 (C) 2 (D) 3 5. [AS4] The number of lines of symmetry for the letter H is . (A) 0 (B) 1 (C) 2 (D) 3 Very Short Answer Type Questions [ ] 6 [AS2] State true or false. . (i) A polygon with all the sides and angles equal is called a regular polygon. [AS2] Fill in the blanks. (ii) A closed figure made from several line segments is called a (iii) A square is a regular . [AS5] Choose the correct answer. (B) Square (D)None of these (iv) is a _____________. (A) Rectangle (C) Trapezium EXERCISE 15.1. LINE SYMMETRY 62
(v) A regular polygon is _____. (A) (B) (C) (D) 7 [AS2] State true or false. (i) The figure is not symmetrical. [] [AS5] Fill in the blanks. (ii) The number of lines of symmetry of the given figure is . (iii) has ____ line(s) of symmetry. EXERCISE 15.1. LINE SYMMETRY 63
[AS2] Choose the correct answer. (iv) has lines of symmetry. (A) 2 (B) 4 (C) 3 (D) 6 (v) have lines of symmetry. (A) Four (B) One (C) Two (D) Three 8 [AS2] State true or false. (i) The figure has only one line of symmetry. (ii) is not a symmetric figure. [AS2] Fill in the blanks. is __________ . (iii) The axis of symmetry of EXERCISE 15.1. LINE SYMMETRY 64
[AS2] Choose the correct answer. (iv) The following figure has lines of symmetry. (A) 4 (B) 2 (C) 3 (D) 0 [AS2] Answer the following questions in one sentence. (v) Given the line of symmetry, draw the other part of the given figure. 9 [AS2] Fill in the blanks. (i) The number of lines of symmetry of an isosceles triangle is . (ii) The number of lines of symmetry of an isosceles trapezium is . (iii) The number of lines of symmetry in a regular pentagon is . (iv) The number of lines of symmetry of a regular decagon is . [AS2] Choose the correct answer. (v) The number of lines of symmetry in a regular hexagon is . (A) 1 (B) 3 (C) 6 (D) 12 10 [AS5] State true or false. [ ] the figure has only two lines of symmetry. (i) EXERCISE 15.1. LINE SYMMETRY 65
(ii) [] have the same mirror image. [AS5] Choose the correct answer. (iii) The mirror image of the given figure is _____. (A) (B) (C) (D)None of these EXERCISE 15.1. LINE SYMMETRY 66
(iv) The mirror image of the given diagram is a _________. (A) Rectangle (B) Square (C) Triangle (D) Rhombus (v) The mirror image of a sphere is in the shape of a ______. (A) Ball (B) Book (C) Rectangle (D)None of these EXERCISE 15.1. LINE SYMMETRY 67
EXERCISE 15.2 ROTATIONAL SYMMETRY 15.2.1 Key Concepts i. If we rotate a figure about a fixed point by a certain angle and the figure looks exactly the same as before, we say that the figure has rotational symmetry. e.g., An equilateral triangle; a square etc. ii. The angle of turning during rotation of a figure is the minimum angle of rotation through which it is to be rotated to get exactly the same figure as the original and is called the angle of rotation. e.g., a) Angle of rotation of an equilateral triangle = 120◦. b) Angle of rotation of a square = 90◦ . iii. All the figures having rotational symmetry of order 1, can be rotated completely through 360° to come back to their original position. So, we say that an object has rotational symmetry only when the order of symmetry is more than 1. e.g., a) The order of rotational symmetry of an equilateral triangle is 3. b) The order of rotational symmetry of a square is 4. 15.2.2 Additional Questions Objective Questions 1. [AS3] The number of lines of symmetry of a square is . (A) 2 (B) 3 (C) 4 (D) Infinitely many EXERCISE 15.2. ROTATIONAL SYMMETRY 68
2. [AS3] The figure that has only 2 lines of symmetry is ______. (A) Equilateral triangle (B) Rhombus (C) Circle (D)None of these 3. [AS3] The number of lines of symmetry of an isosceles triangle is . . (A) 1 (B) 2 (C) 3 (D) 4 4. [AS3] The figure that has no line of symmetry is _______. (A) Square (B) Rhombus (C) Circle (D) Parallelogram 5. [AS3] The number of lines of symmetry of a regular pentagon is (A) 3 (B) 4 (C) 5 (D) 6 Short Answer Type Questions 6(i) [AS2] Name the quadrilaterals which have both line and rotational symmetry of order more than 1. (ii) [AS2] After rotating by 60◦ about a centre, a figure looks exactly the same as itself. At what other angles will this happen for the figure? 7(i) [AS2] Can figures have a rotational symmetry of order more than 1 if their angles of rotation are (a) 45 ◦? (b) 17 ◦? EXERCISE 15.2. ROTATIONAL SYMMETRY 69
(ii) [AS2] Complete the given table. Shape Centre of Order of Angle of Rectangle Rotation Rotation Rotation Rhombus Equilateral Triangle Regular Hexagon Semicircle 8(i) [AS3] Some of the letters of the English alphabet are symmetrical. Which upper case letters such as the letter E have just one line of symmetry? Which upper case letters such as the letter I have a rotational symmetry of order 2? Complete the given table. Alphabet Line Number Rotational Order of Letters Symmetry of lines of Symmetry Rotational Symmetry Symmetry Z Nil Yes 2 0 S H Yes Yes O Yes Yes E Yes N Yes C EXERCISE 15.2. ROTATIONAL SYMMETRY 70
(ii) [AS5] Give the order of rotational symmetry for each figure: 9(i) [AS2] Observe the given figures and give the order of the rotational symmetry of an equilateral triangle. How many positions are there at which the triangle looks exactly the same, when rotated about its centre by 120◦ ? EXERCISE 15.2. ROTATIONAL SYMMETRY 71
EXERCISE 15.3 LINE SYMMETRY AND ROTATIONAL SYMMETRY 15.3.1 Key Concepts i. Some shapes only have line symmetry and some have only rotational symmetry and some have both. ii. Squares, equilateral triangles and circles have both line symmetry and rotational symmetry. 15.3.2 Additional Questions Objective Questions 1. [AS3] The order of rotational symmetry of an equilateral triangle is . (A) 1 (B) 2 (C) 3 (D) 4 2. [AS3] A rectangle has rotational symmetry of order . (A) 0 (B) 1 (C) 3 (D) 2 3. [AS3] The angle of rotational symmetry of a square is . (A) 180◦ (B) 270◦ (C) 90◦ (D) 60◦ EXERCISE 15.3. LINE SYMMETRY AND ROTATIONAL SYMMETRY 72
4. [AS3] The order of rotational symmetry of a regular hexagon is . (A) 3 (B) 4 (C) 5 (D) 6 5. [AS3] All figures have rotational symmetry of order . (A) 0 (B) 1 (C) 2 (D) 3 Long Answer Type Questions 6 [AS5] Draw a triangle which has a) exactly one line of symmetry. b) exactly two lines of symmetry. c) exactly three lines of symmetry. d) no line of symmetry. Draw a rough sketch in each case. EXERCISE 15.3. LINE SYMMETRY AND ROTATIONAL SYMMETRY 73
—— Project Based Questions —— (i) Take a tape and with the help of one of your family members measure the length and breadth of your study room, your hall and your bed room. Find the ratio of length and breadth in each case and note it down in the form of a table. (ii) Collect the information of the monthly income and expenditures on various things from your parents and represent them in the form of a pie diagram using different colours. PROJECT BASED QUESTIONS 74
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