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Important Questions for CBSE Class 8 Maths Chapter 10 - Visualising Solid Shapes

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Last updated date: 19th May 2024
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CBSE Class 8 Maths Important Questions for Visualising Solid Shapes - Free PDF Download

CBSE Class 8 Maths Chapter 10 Visualising Solid Shapes is a crucial part of the syllabus of this subject that explains different regular and irregular solids and their features. The exercises have been set by following these concepts. After completely preparing this chapter, students will need the important questions designed by the subject experts of Vedantu to practice. These questions come with solutions for adding more convenience to the practice sessions.


Free PDF download of Important Questions with solutions for CBSE Class 8 Maths Chapter 10 - Visualising Solid Shapes prepared by expert Mathematics teachers from the latest edition of CBSE (NCERT) books is available on Vedantu. Register online for Maths tuition on Vedantu.com to score more marks in your examination.


Vedantu is a platform that provides free NCERT Solutions and other CBSE study materials for students. Students can register and get access to the best and most reliable source of study materials specially made by master teachers at Vedantu. Subjects like Science, Maths, and English will become easy to study if you have access to NCERT Solution for Class 8 Science, Maths solutions and solutions of other subjects.


You can also download NCERT Solutions Class 8 Maths to help you to revise and complete syllabus and score more marks in your examinations. 

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Study Important Questions for Class 8 Maths Chapter 10 – Visualising Solid Shapes

Very Short Answer Type Questions (1 Mark)

1. A three dimensional shape is $\_\_\_\_\_\_\_\_\_$object. 

Ans: Solid


2. The most important part of a map is the $\_\_\_\_\_\_\_\_\_$

Ans: Scale


3. What are three views in a solid figure? 

Ans: Front view, side view and top view


4. Name of the solid whose net diagram is given below


Cube


(a) Pyramid

(b) Cone

(c) Cube

(d) Cuboid

Ans: (c) Cube


5. The number of triangular face's of a triangular prism is $\_\_\_\_\_\_\_\_\_$

(a) $1$

(b) $4$

(c) $2$

(d) $3$

Ans: (c) $2$


Short Answer Type Questions (2 – Marks)

6. What are regular polyhedrons?

Ans: A polyhedron is called regular if its faces are made up of regular polygons and the same number of faces meet a vertex.


7. Give two basic differences between a prism and a pyramid?

Ans: (a) Pyramid is a polyhedron in which the base is a polygon whereas a prism is a polyhedron in which the base and top are regular polygons.

(b) The lateral surface are parallelograms in a prism whereas in a pyramid the lateral surfaces are triangles.


8. Give two examples of $2\;{\text{d}}$ and $3\;{\text{d}}$ shapes each.

Ans: $2\;{\text{d}}$ shapes : circle, square.

$3\;{\text{d}}$ shapes = pyramid, cone.

9. How many number of squares are visible in top view and front view of the given figure.


Squares


Ans: Top view $ = 6$ squares

Front view $ = 4$ squares


10. In the given solid identify the top, front and side view.


Solid


(a)


side view


(b)


Front view


(c)


Top view


Ans:

(a) side view

(b) front view

(c) top view


11. Give Euler's formula and explain each term in it. 

Ans: In a polyhedron, the relationship between the number of faces $({\text{F}})$, vertices $({\text{V}})$, and edges $({\text{E}})$ is given by $F + V - {\text{E}} - 2$.


12. Write the number of faces, number of vertices and number of edges of a prism with rectangular base


Rectangular base


Ans: No. of faces $ = 6$ 

No. of vertices $ = 8$ 

No. of Edges $ = 12$


13. Write the number of faces, number of vertices and number of edges of a pyramid with hexagonal base.


A pyramid with hexagonal base


Ans:

No. of faces $ = 7$ 

No. of vertices $ = 7$

No. of edges $ = 12$


14. In a polyhedron there are $8$ vertices and $12$ edges. Find its number of faces. 

Ans:

${\text{F}} + {\text{V}} - {\text{E}} = 2$

$F + 8 - 12 = 2$

$F = 2 + 12 - 8$

$F = 6$


15. A pyramid with square base has $5$ faces and $8$ edges. By Euler's formula, find the vertices of the pyramid. 

Ans: For a pyramid,

$F = 5,{\text{ }}E = 8,{\text{ }}V = ?$

Using Euler's formula, 

$F + V - E = 2$ 

$5 + V - 8 = 2$

$V = 2 + 8 - 5$

$V = 5$


Short Answer Type Questions (3 – Marks)

16. Draw the front view, side view and top view of the given objects.


An objects


Ans:

(a) Front view


Front view


(b) Top view


Top view


(c) Side view


Side view


17. Can a polyhedron have $10$ faces, $20$ edges and $15$ vertices? Justify your answer.

Ans: $F = 10,{\text{ }}E = 20$ and $V = 15$

Using Euler's formula, 

$F + V - E = 2$

L.H.S:

$F + V - E = 10 + 15 - 20$

$F + V - E = 5$

$\therefore F + V - E \ne 2$

This polyhedron is not possible.


18. Match the following pictures with their shapes.

Ans:

Picture (object)

Shape

(1)

A cone taken out of a cylinder

(a) A cone taken out of a cylinder

(2)

Two rectangular cross paths inside a rectangular park

(b) Two rectangular cross paths inside a rectangular park

(3)

A circular path around a circular ground

(c) A circular path around a circular ground

Ans: $1 - b,{\text{ }}2 - c,{\text{ }}3 - a$


19. Define

(a) Face

(b) Edge

(c) Vertex 

Ans: (a) Face$ - {\text{A}}$$3\;{\text{d}}$ solid object is made up of flat surfaces or polygonal regions known as faces.

(b) Edge: In $3\;{\text{d}}$ solid objects, the faces meet at edges.

(c) Vertex: The point where all edges meet is known as a vertex.


20. By using Euler's formula find the unknown?

(a) vertices$ = 12$, Faces$ = 4$, Edges $ - ?$

(b) Faces$ = 5$, Edges$ = 8$, Vertices $ = ?$

(c) Edges$ = 2$, Vertices$ = 3$, Faces $ = ?$ 

Ans: Using Euler 's formula: 

$F + V - E = 2$

(a) $4 + 12 - E = 2$

$E = 16 - 2 = 14$

(b) $5 + V - 8 = 2$

$V = 2 + 8 - 5 = 5$

(c) $F + 3 - 2 = 2$

${\text{F = }}2 + 2 - 3 = 1$


Long Answer Type Questions (4 – Marks)

21. Write an examples for tetrahedron and write the number of triangular faces, vertices and edges. Show it verifies Euler’s formula.


A pyramid


Ans: Example for tetrahedron$ = $Tent 

Number of triangular faces $ = 4$

Number of Vertices $ = 4$

Number of Edges $ = 6$ 

Euler's formula:

$F + V - E = 2$

$4 + 4 - 6 = 2$

$2 = 2$ 

Hence verified.


22. Write an example for Hexahedron with number of faces, vertices and edges. Show it verifies Euler's formula.


Hexahedron


Ans: Example for Hexahedron$ - $Cube (Die) 

Number of faces $ = 6$

Number of Vertices $ = 8$

Number of Edges $ = 12$

Euler’s formula:

$F + V - E = 2$ 

$6 + 8 - 12 = 2$

$14 - 12 = 2$

$2 = 2$ 

Hence verified.


23. Write a prism with square base and a pyramid with rectangular base. Write the number of edges in each case.

Ans: (a) A prism having a square base has $12$ edges.


A prism with square base


(b) A pyramid with rectangular base has $8$ edges.


A pyramid with rectangular base


24. Match the net’s with appropriate solids.

(a)

A sylinder

(i) 

A pyramid base


(b) 

A cone


(ii) 

Cube


(c)

square

(iii) 

A sylindr with circular base


(d) 

A pyramid


(iv) 

A triangle with circular base



Ans: 

\[(a) - \left( {iii} \right)\]

\[(b) - \left( {iv} \right)\]

\[(c) - \left( {ii} \right)\]

\[(d) - \left( i \right)\]


25. What cross sections are obtained when

(i) vertical cut

(ii) horizontal cut

(a) An ice cream cone

(b) A die

(c) A round apple

(d) A circular pipe are done with 

Ans:

S. No

Name of the article

Figure

Vertical cut

Horizontal cut

(a)

An ice cream cone 

An ice cream cone

Vertical cut of an ice cream cone

Horizontal cut an ice cream cone

(b)

A Die

A Die

Vertical cut of a Die

Horizontal cut of a die

(c)

A round apple

A round apple

Vertical cut of a round apple

Horizontal cut of a round apple

(d)

A circular pipe

A circular pipe

Vertical cut of a circular pipe

Horizontal cut of a circular pipe


26. What is the difference between a cube and a cuboid?

Ans. A cube has all sides equal in length, while a cuboid has different dimensions for length, width, and height.


27. How many faces, edges, and vertices does a cylinder have?

Ans. A cylinder has two flat circular faces, one curved surface, three edges, and two vertices.


28. Explain the concept of an octahedron.

Ans. An octahedron is a three-dimensional figure with eight triangular faces, twelve edges, and six vertices.


29. How can you determine the volume of a rectangular prism?

Ans. The volume of a rectangular prism is calculated by multiplying its length, width, and height.


30. Can a pyramid have a circular base?

Ans. Yes, a pyramid can have a circular base. This type of pyramid is known as a cone, and it is characterized by a single circular base and a pointed top.


Significance of CBSE Class 8 Maths Chapter 10 Visualising Solid Shapes Important Questions.

The important questions have been formulated by following the latest CBSE Class 8 Maths syllabus to cover all the topics taught in this chapter. It means the students will find problems related to all the mathematical principles taught in this chapter and can practice solving them. Solving these questions will help students understand how to use these concepts skillfully to find accurate answers.


Advantages of Class 8 Maths Chapter 10 Visualising Solid Shapes Important Questions

Embarking on the study of Class 8 Mathematics, Chapter 10 - "Visualising Solid Shapes," students encounter a realm that intertwines geometry with three-dimensional structures. Recognizing the significance of mastering this chapter, the compilation of important questions by Vedantu emerges as a valuable resource. In this introduction, we'll explore the advantages these crucial questions bring to students, unraveling the complexities of visualizing solid shapes and reinforcing their grasp on this fundamental mathematical concept.


1. Strategic Question Solving: Solving important questions in Class 8 Maths Chapter 10 aids in applying mathematical concepts effectively.

2. Gap Identification: Compare your answers to solutions to identify gaps in your preparation and focus on areas needing improvement.

3. Stepwise Problem-Solving: Emphasize stepwise methods to solve questions, enhancing problem-solving and answering skills.

4. Doubt Resolution: Utilize solutions to resolve doubts related to these questions, ensuring a clearer understanding of the material.

5. Efficient Study Focus: Focus on key topics for efficient studying, reinforcing fundamental concepts crucial for exams.

6. Exam Preparedness: Prepare for exams with reduced anxiety, benefiting from effective time management techniques.

7. Self-Assessment and Progress Tracking: Enable self-assessment and track progress using a strategic approach, ultimately boosting confidence.

8. Comprehensive Understanding: Cover a wide range of topics for comprehensive understanding, supporting exam preparation and overall academic success.


Download CBSE Class 8 Maths Chapter 10 Visualising Solid Shapes Important Questions PDF

Get the free PDF version of these important questions and solutions and complete your study material for this chapter. Practice solving them and take your preparation to the next level.


Conclusion

Visualising Solid Shapes is an integral part of Class 8 Maths and plays a crucial role from an examination perspective. The important questions for Class 8 Maths, as discussed by NCERT, cover a wide range of topics within the subject. They also provide a concise guide to critical points and details related to the topic.


A solid understanding of each section of Class 8 Maths is fundamental as it forms the basis for higher-level studies. However, this section primarily focuses on important questions within the context of Class 8 Maths.

FAQs on Important Questions for CBSE Class 8 Maths Chapter 10 - Visualising Solid Shapes

1. Why should I learn solid shapes?

Studying this chapter will enable students to learn more about regular and irregular solids and their features. They can easily identify them later and recall these features.

2. How can I master the problem-solving skills for this chapter?

Focus on solving all the questions of the NCERT exercises first. Then, solve these important questions and compare your answers to the solutions.

3. What is the best way to prepare Class 8 Maths Chapter 10 Visualising Solid Shapes?

Study the theoretical part first. Focus on how they are explained and used to solve the exercise questions by referring to the NCERT solutions. Practice solving the important questions to test your skills. This is how you can prepare this chapter well.

4. Can I use the solutions to revise this chapter?

Following the solutions for these questions will help you recall the methods of solving the important questions and help you revise this chapter.

5. Is it necessary to solve important questions for Class 8 Maths Chapter 10, Visualising Solid Shapes?

The more you practice solving such questions, the better you will score in the exams.