NCERT Exemplar Class 8 Maths Solutions for Chapter 6 - Visualising Solid Shapes

NCERT Exemplar Solutions Class 8 Maths Chapter 6 – Free PDF Download

NCERT Exemplar Solutions for Class 8 Maths Chapter 6 Visualising Solid Shapes are provided here for students to prepare well for exams. These exemplars solutions are designed by experts in accordance with the latest CBSE syllabus (2023-2024), which cover all the topics of Maths Chapter 6 of Class 8. The chapter, Visualizing Solid Shapes, is about learning different types of shapes in 2 and 3 dimensions. To master the concepts of this chapter, students are advised to solve the questions from the NCERT Exemplar for Class 8 Maths Visualizing Solid Shapes. Solving these Exemplar problems for Class 8 will boost their exam preparation and score high in the annual exam. Below is the list of topics covered in Chapter 6 of Class 8 Maths.

• Difference between 2D and 3D figures
• Different Types of 3D Shapes
• Faces, Edges and Vertices

Apart from these exemplars, we provide notes, exemplar books, NCERT Solutions for Class 8 Maths and question papers to help students practise well for final exams. Besides, students are advised to solve sample papers and previous years’ question papers which gives an idea of the types of questions asked in the annual exam from Chapter 6, Visualising Solid Shapes.

NCERT Exemplar Class 8 Maths Solutions Chapter 6 Visualising Solid Shapes:-Download PDF Here

Access NCERT Exemplar Solutions for Class 8 Maths Chapter 6

Exercise Page: 181

In each of questions 1 to 21, out of four options, only one is correct. Write the correct answer.

1. Which of the following is not a polyhedron?

Solution:-

(c)

By definition, a polyhedron is regular if its faces are congruent regular polygons and the same number of faces meet at each vertex.

2. Which of the following will not form a polyhedron?

(a) 3 triangles (b) 2 triangles and 3 parallelograms

(c) 8 triangles (d) 1 pentagon and 5 triangles

Solution:-

(a) 3 triangles

3 triangles will not form a polyhedron because it must have more than four faces. So, it is not possible in 3 triangles which have 3 faces only.

3. Which of the following is a regular polyhedron?

(a) Cuboid (b) Triangular prism

(c) Cube (d) Square prism

Solution:-

(c) Cube

Because, a cube is a platonic solid because all six of its faces are congruent squares.

4. Which of the following is a two Dimensional figure?

(a) Rectangle (b) Rectangular Prism

(c) Square Pyramid (d) Square Prism

Solution:-

(a) Rectangle

A rectangle is a two dimensional figure. It has length and breadth.

5. Which of the following can be the base of a pyramid?

(a) Line segment (b) Circle (c) Octagon (d) Oval

Solution:-

(c) Octagon

A pyramid is a polyhedron whose base is a polygon, and lateral faces are triangles.

6. Which of the following 3D shapes does not have a vertex?

(a) Pyramid (b) Prism (c) Cone (d) Sphere

Solution:-

Sphere.

The faces meet at edges which are line segments, and the edges meet at a point called vertex. Since a sphere has no vertex and no edges.

7. Solid having only line segments as its edges is a

(a) Polyhedron (b) Cone (c) Cylinder (d) Polygon

Solution:-

(a) 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.

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

Solution:-

(c) 8

We have,

Euler’s formula for any polyhedron is, F + V – E = 2

Given, F = V = 5

Where, face (F) = 5, Vertex (V) = 5, Edge (E) =?

Then,

5 + 5 – E = 2

10 – E = 2

10 – 2 = E

Edges (E) = 8

9. Which of the following is the top view of the given shape?

Solution:-

(a)

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

Solution:-

(a) M

11. Which of the nets given below will generate a cone?

Solution:-

Option (a) has a circular base, which gives a cone.

12. Which of the following is not a prism?

Solution:-

(b)

By observing option (b) figure, the bottom and top faces are not congruent polygons.

13. We have 4 congruent equilateral triangles. What do we need more to make a pyramid?

(a) An equilateral triangle.

(b) A square with the same side length as of triangle.

(c) 2 equilateral triangles with side lengths the same as triangles.

(d) 2 squares with side lengths the same as triangles.

Solution:-

(b) A square with the same side length as of triangle.

We have to add a square with the same side length as of triangle to make a pyramid. As we know, a pyramid is a polyhedron whose base is a polygon and whose lateral faces are triangles.

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

Solution:-

(b) 24 cm

Given, side of a square garden = 30m

Scale to draw the garden picture is 1cm: 5m

So, the perimeter of the square garden is = 4 × 30

= 120m

Then,

Perimeter to draw garden in picture = 120/5

= 24 cm

15. Which of the following shapes has a vertex?

Solution:-

(c)

The edges meet at a point called the vertex.

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 the school and the bookshop is

(a) 1.25 (b) 2.5 (c) 2 (d) 1.1

Solution:-

Given, Scale = 1 cm: 0.5km

Then the actual distance between the school and the bookshop is = 2.2 × 0.5

= 1.1 cm

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

Solution:-

(d) V = 4, F = 6, E = 6

We have,

Euler’s formula for any polyhedron is, F + V – E = 2

Where, face (F) = 6, Vertex (V) = 4, Edge (E) =6

Then,

6 + 4 – 6 = 2

LHS 6 + 4 -6

10 – 6

4

RHS= 2

By comparing LHS and RHS

LHS ≠ RHS

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

Solution:-

(b) 1: 10

From the question, it is given that,

An architect has shown the height of the room as 33 cm

The actual height of the room is 330 cm

Then, the scale used by an architect is = Drawn size/actual size

= 33/330 … [divide both by 33]

= 1/10

= 1: 10

19. The following is the map of a town. Based on it answer questions 19-21.

The number of hospitals in the town is

(a) 1 (b) 2 (c) 3 (d) 4

Solution:-

(b) 2

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

Solution:-

(d) 3: 2

By observing the given map,

The number of general stores = 6

The number of ground = 4

Then,

The ratio of the number of general stores and that of the ground is = 6/4

= 3/2

= 3: 2

21. According to the map, the number of schools in the town is

(a) 4 (b) 3 (c) 5 (d) 2

Solution:-

(c) 5

In questions 22 to 41, fill in the blanks to make the statements true.

22. Square prism is also called a _______.

Solution:-

A square prism is also called a cube.

A cube is a platonic solid because all six of its faces are congruent squares.

23. Rectangular prism is also called a ________.

Solution:-

A rectangular prism is also called a Cuboid.

24. In the figure, the number of faces meeting at B is ________.

Solution:-

The number of faces meeting at B is 4.

25. A pyramid on an n sided polygon has ______ faces.

Solution:-

A pyramid on an n sided polygon has n+1 faces.

26. If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.

Solution:-

If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is 30.

We have,

Euler’s formula for any polyhedron is, F + V – E = 2

Given, F = 12, V = 20

Where, face (F) = 12, Vertex (V) = 20, Edge (E) =?

Then,

12 + 20 – E = 2

32 – E = 2

32 – 2 = E

Edges (E) = 30

27. The given net can be folded to make a ______.

Solution:-

The given net can be folded to make a prism.

28. A solid figure with only 1 vertex is a ______.

Solution:-

A solid figure with only 1 vertex is a cone.

29. Total number of faces in a pyramid which has eight edges is______.

Solution:-

The total number of faces in a pyramid which has eight edges is 5.

30. The net of a rectangular prism has ______ rectangles.

(Hint: Every square is a rectangle, but every rectangle is not a square.)

Solution:-

The net of a rectangular prism has six rectangles.

31. In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the ______ face.

Solution:-

In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the same face.

32. If 4 km on a map is represented by 1 cm, then 16 km is represented by ______ cm.

Solution:-

If 4 km on a map is represented by 1 cm, then 16 km is represented by 4 cm.

= 16/4

= 4 cm

33. If the 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 ______.

Solution:-

If the 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 1: 4400000

From the question, it is given that,

Actual distance between two places A and B is = 110km

Distance is represented on a map by = 25 mm

So, the scale used is = Size drawn on map/ actual distance

= 25 mm/110 km

We know that, 1km = 1000m

1m = 100cm

1cm = 10mm

1 km = 10,00,000

So, 110km = 11,00,00,000 mm

Therefore = 25/11,00,00,000

= 1/4400000

= 1: 4400000

34. A pentagonal prism has ______ faces.

Solution:-

A pentagonal prism has 7 faces.

35. If a pyramid has a hexagonal base, then the number of vertices is ______.

Solution:-

If a pyramid has a hexagonal base, then the number of vertices is 7.

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