NCERT Exemplar Solutions Class 7 Maths Chapter 12 Practical Geometry Symmetry & Visualising Solid Shapes

NCERT Exemplar Class 7 Maths Book PDF Download Chapter 12

Multiple Choice Questions (MCQs)

Question 1: A triangle can be constructed by taking its sides as

(a) 1.8 cm, 2.6 cm, 4.4 cm

(b) 2 cm, 3 cm, 4 cm

(c) 2.4 cm, 2.4 cm, 6.4 cm

(d) 3.2 cm, 2.3 cm, 5.5 cm

Solution:

(b) Triangle can be constructed only if they satisfy the given condition. Sum of two sides > Third side Clearly, only option (b) satisfies the given condition.
(2 + 3)cm > 4 cm i.e. 5 cm > 4 cm

Question 2: A triangle can be constructed by taking two of its angles as

(a) 110°, 40°

(b) 70°, 115°

(c) 135°, 45°

(d) 90°, 90°

Solution:

(a) We know that, the sum of all the angles of a triangle is equal to 180°. So, sum of any two angles of a triangle should be less than 180°.

110°+ 40° = 150° i.e. less than 180°.

70° + 115° = 185° i.e. greater than 180°.

135° + 45°= 180° i.e. equal to 180°.

90° + 90°= 180° i.e. equal to 180°.

Hence, (a) is the correct option.

Question 3: The number of lines of symmetry in the figure given below is

(a) 4

(b) 8

(c) 6

(d) infinitely many

Solution: (c) given figure has 6 lines of symmetry.

Question 4: The number of lines of symmetry in the figure given below is

(a) 1 (b) 3 (c) 6 (d) infinitely many

Solution: (b) The given figure has 3 lines of symmetry.

Question 5: The order of rotational symmetry in the figure given below is

(a) 4 (b) 8 (c) 6 (d) infinitely many

Solution: (c) Since, the number of times a figure fits onto itself in one full turn is called order of rotational symmetry.
Therefore, the given figure has rotational symmetry of order 6.

Question 6: The order of rotational symmetry in the figure given below is

(a) 4 (b) 2 (c) 1 (d) infinitely many

Solution: (b) Since, the number of times a figure fits onto itself in one full turn is called order of rotational symmetry.
So, the given figure has rotational symmetry of order 2.

Question 7: The name of the given solid in the figure is

(a) triangular pyramid

(b) rectangular pyramid

(c) rectangular prism

(d) triangular prism

Solution: (b) it is a combination of rectangle and pyramid. Hence, (b) is the correct option.

Question 8: The name of the solid in figure is

(a) triangular pyramid (b) rectangular prism

(c) triangular prism (d) rectangular pyramid

Solution: (c) It is a combination of triangle and prism. Hence, (c) is the correct option.

Question 9: All faces of a pyramid are always

(a) triangular (b) rectangular (c) congruent (d) None of these

Solution: (d) The faces of a pyramid can be triangular and rectangular. Hence, (d) is the correct option.

Question 10: A solid that has only one vertex is

(a) pyramid (b) cube (c) cone (d) cylinder

Solution: (c) The cone is the shape, that has only one vertex. Hence, (c) is the correct option.

Question 11: Out of the following which is a 3-D figure?

(a) Square (b) Sphere (c) Triangle (d) Circle

Solution: (b) Square, triangle and circle are 2-D figures while sphere is the 3-D figure. Hence, (b) is the correct option.

Question 12: Total number of edges a cylinder has

(a) 0 (b) 1

(c) 2 (d) 3

Solution: (c) The cylinder has 2 edges. Hence, (c) is the correct option.

Question 13: A solid that has two opposite identical faces and other faces as parallelograms is a

(a) prism (b) pyramid

(c) cone (d) sphere

Solution: (a) Prism has two opposite identical faces and other faces as parallelograms.

Question 14: The solid with one circular face, one curved surface and one vertex is known as

(a) cone (b) sphere

(c) cylinder (d) prism

Solution: (a) Cone has one circular face, one curved surface and one vertex.

Question 15: If three cubes each of edge 4 cm are placed end to end, then the dimensions of resulting solid are

(a) 12 cm x 4 cm x 4 cm (b) 4 cm x 8 cm x 4 cm

(c) 4 cm x 8 cm x 12 cm (d) 4 cm x 6 cm x 8 cm

Solution: (a) If the three cubes are placed end to end that means length is increased. The new cuboid having dimensions 12cmx4cmx4cm Hence, (a) is the correct option.

Question 16: When we cut a corner of a cube as shown in the figure, we get the cutout piece as

(a) square pyramid (b) trapezium prism

(c) triangular pyramid (d) a triangle

Solution: (c) If we cut a corner of a cube, then we get cut-out of a piece in the form of triangular pyramid.

More Resources for class 7

• NCERT Solutions for Class 7
• NCERT Solutions for Class 7 Maths
• NCERT Solutions for Class 7 Science
• NCERT Solutions for Class 7 Social Science
• NCERT Solutions for Class 7 English

Question 17: If we rotate a right-angled triangle of height 5 cm and base 3 cm about its height a full turn, we get

(a) cone of height 5 cm, base 3 cm

(b) triangle of height 5 cm, base 3 cm

(c) cone of height 5 cm, base 6 cm

(d) triangle of height 5 cm, base 6 cm

Solution: (a) If we rotate a right-angled triangle of height 5 cm and base 3 cm about its height a full turn, then we get a cone of height 5 cm and base 3 cm.

Question 18: If we rotate a right-angled triangle of height 5 cm and base 3 cm about its base/we get

(a) cone of height 3 cm and base 3 cm

(b) cone of height 5 cm and base 5 cm

(c) cone of height 5 cm and base 3 cm

(d) cone of height 3 cm and base 5 cm

Solution: (d) If we rotate a right-angled triangle of height 5 cm and base 3 cm about its base, we get a cone of height 3 cm and base 5 cm.

Question 19: When a torch is pointed towards one of the vertical edges of a cube you get a shadow of cube in the shape of

(a) square (b) rectangle but not a square

(c) circle (d) triangle

Solution: (b) When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of rectangle but not a square.

Question 20: Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle?

(a) 3 cm, 4 cm, 6 cm (b) 9 cm, 16 cm, 26 cm

(c) 1.5 cm, 3.6 cm, 3.9 cm (d) 7 cm, 24 cm, 26 cm

Solution: (c) The sides of right-angled triangle must satisfy Pythagoras theorem. (Hypotenuse)² = (Base)² + (Perpendicular)²

Note: Hypotenuse is the largest side of all the sides. So, check all options by putting the values in above formula.

Let us check all the options.

(a) (6)² = (3)² + (4)²

36=9+16

36 ≠ 25

(b) (26)² = (16)² + (9)² = 676

= 256 + 81

676 ≠ 337

(c) (3.9)² = (1.5)² + (3.6)² = 15.21

= 2.25+12.96

=15.21 = 15.21 (satisfied)

(d) (26)² = (7)² + (24)²

= 676 = 49+576

=676 ≠ 625

Clearly, option (c) is correct.