Important Questions Class 8 Maths Chapter 10

Important Questions Class 8 Mathematics Chapter 10 – Visualising Solid Shapes

Daily, we visualise different shapes of objects, which can be triangles, squares, circles, rectangles,or even a combination of these shapes. In the previous class, you learned about plane shapes (two-dimensional shapes) and solid shapes (three-dimensional shapes). Chapter 10 of Class 8 Mathematics is about Visualising Solid Shapes. It teaches you the difference between two-dimensional and three-dimensional shapes. 

The key topics covered in Chapter 10 are discussed in the below points,

• Plane shapes are called two-dimensional shapes, as they have only length and breadth measurements, for example, triangles, rectangles, squares, etc. 
• Solid shapes are three-dimensional shapes with length, breadth, and height measurements—for example, cubes, cylinders, spheres, etc.
• The three-dimensional objects look different from different positions. 
• Mapping surrounding areas: This section explains how to read and understand the maps. A map shows the location of an object or place to other objects/places without any perspective of view, i.e. irrespective of the observer’s position. 
• Polyhedron solid shapes are made up of faces, edges, and vertices. The faces are referred to as polygonal regions of solid objects. The Edges are the line segments where the faces meet, and the points where all the edges meet are called vertices. Some examples of polyhedron shapes are prisms, pyramids, and cuboids.
• The two types of polyhedrons are convex polyhedrons and regular polyhedrons. 
• Euler’s formula F + V – E = 2 is always true for any polyhedron, where ‘F’ is the number of faces, V is the number of vertices, and E is the number of edges.

Extramarks is one of the top e-learning portals for Class 1 to Class 12 students preparing for their board examinations. Various study and practise materials are prepared after extensive research by the subject experts. Learning through NCERT solutions and Mathematics Class 8 Chapter 10 Important Questions  on the Extramarks website will help you  understand the abstract idea of solid shapes and how to identify them. 

A full list of Chapter 10 Class 8 Mathematics Important Questions is collated from the CBSE sample papers, NCERT exemplars, NCERT textbook, and other genuine sources for students to help practise various questions from the chapter before facing their final examination.

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Important Questions Class 8 Mathematics Chapter 10 – With Solutions

Extramarks provides Important Questions Class 8 Mathematics Chapter 10 with detailed solutions to help students get in-depth knowledge of chapter concepts and identify different dimensions of shapes and geometrical figures. Students should practise these questions rigorously to be confident,

while answering the questions in final examinations and scoring well. 

The below consists of few sample questions and their solutions from our question bank of Class 8 Mathematics Chapter 10 Important Questions:

Question 1. A pyramid is a polyhedron with lateral faces of,

(a) Triangles

(b) Rectangles 

(c) Rhombuses or Rhombi

(d) Parallelograms 

Answer 1. (a) triangle.

Explanation: A pyramid is a type of polyhedron solid shape whose base is a polygon and the lateral faces are triangles with a common vertex.

Question 2. Using Euler’s formula, find the unknown.

Answer 2. Euler’s formula is F + V – E = 2

Solution 1 : Finding the unknown value F where V = 6 and E = 12

                     F + 6 – 12 = 2

                     F – 6 = 2

                     F = 2 + 6 = 8                    

Solution 2: Finding the unknown value V where F = 5 and E = 9

                     5 + V – 9 = 2

                     V – 4 = 2

                     V = 2 + 4 = 6

Solution 3: Finding the unknown value E where F = 20 and V = 12

                     20 + 12 – E = 2

                     32 – E = 2

                     E = 32 – 2 = 30

Question 3. In a regular polyhedron, ______ number of faces meet at each vertex.

Answer 3. Same

Question 4. Can a polyhedron have its faces

(a) Three triangles?

(b) Four triangles?

(c) A square and four triangles?

Answer 4.

(a) No. A polyhedron requires at least four faces, as all the faces should meet at the same point, called vertices.

(b) Yes. A triangular pyramid with three triangle faces and one triangle base can be made using four triangles.

(c) Yes. It can form a square pyramid with one square base and four triangles.

Question 5. The distance between City R and City T on a map is 8 cm. Find the actual distance between City R and City T; if the scale represents 1 cm = 200 km

Answer 5. Given that 1 cm = 200 km as measured on the scale, then

                   the actual distance between City R and City T in kilometers is,

                   8 cm x 200 km = 1600 km.

Question 6. The height of a building is 10 m. The height of this building drawn on the map is 10 cm. Explain the scale used for the map.

Answer 6 : Scale of map = Size drawn

                                                Actual size

                                             = 10cm

                                                1000cm  (because 10 m = 1000 cm)

                                             =   1

                                                100

                                         Thus, the scale is 1:100.

Question 7. The actual distance between the two cities is 60m. Find the distance drawn on the map if the scale on a map is 1 mm: 6 m. 

Answer 7. Given that the scale on the map is 1 mm: 6 m

                    To find the distance drawn on the map for an actual distance of 60 m,

                    Scale of map = distance drawn

                                                Actual distance

                                        1     =  distance drawn

                                        6              60 m

                                        distance drawn =   1  x 60  = 10 mm

                                                                          6 

Thus, the distance on the map for the actual distance of 60 m is

10 mm.

Question 8. Question 8. Having four 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 a triangle.

(c) Two equilateral triangles with side lengths the same as a triangle.

(d) Two squares with side lengths the same as a triangle.

Answer 8. (b) A square with the same side length as a triangle.

Explanation : 

A pyramid is made with a polygonal base and equilateral triangular lateral faces.

We need a polygon with all four equal side lengths as a triangle because we have four congruent equilateral triangles.Hence, the required polygon is a square. It has four equal sides, and the triangle lies on the edges of the square. Below is a picture of a pyramid with a square base and four equilateral triangle faces.  

Question 9. Can a polyhedron be made with ten faces, twenty edges and fifteen vertices?

Answer 9.   For any polyhedron, Euler’s formula F + V – E = 2 should always be true.

                     Let us verify the formula with the given number of faces, edges and vertices.

                      F + v – E = 2

                      10 + 15 – 20 = 2

                      25 – 20 = 5 ≠ 2

Since F + V – E is not equal to 2 for the above-given inputs, a polyhedron cannot be made with ten faces, twenty edges and fifteen vertices.

Question 10. In a three-dimensional shape, a diagonal is a line segment that joins two vertices that do not lie on the ______ face.

Answer 10. Same 

Question 11. State whether the following statements are true (T) or false (F). Correct the false statements.

• The other name for a cuboid is a tetrahedron.

•  A polyhedron can have three faces.

•  A polyhedron with the least number of faces is a triangular pyramid.

• A regular octahedron has eight congruent faces, which are isosceles triangles.

Answer 11. 

(1) True

(2) False. A polyhedron requires at least four faces, as all the faces should meet at the same point, called vertices.

(3) False. A triangular pyramid is a polyhedron consisting of four faces.

(4) False. A regular octahedron has eight congruent faces of equilateral triangles.

Question 12. 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

Answer 12. (d) V = 4, F = 6, E = 6

Explanation: Euler’s formula F + V – E = 2 can be used to verify which set among the above options cannot make a polyhedron.

1. With V = 4, F = 4, E = 6

4 + 4 – 6 = 2

8 – 6 = 2

2 = 2

Option (a) is true for a polyhedron

1. With V = 6, F = 8, E = 12

8 + 6 – 12 = 2

14 – 12 = 2

2 = 2

Option (b) is true for a polyhedron

      (c) With V = 20, F = 12, E = 30

             12 + 20 – 30 = 2

             32 – 30 = 2

             2 = 2

 Option (c) is true for a polyhedron

     (d) With V = 4, F = 6, E = 6

             6 + 4 – 6 = 2

             10 – 6 = 2

             4 ≠ 2

 Hence option (d) is not true for a polyhedron

Question 13. Fill in the blanks for the below sentences

• A pyramid on an n-sided polygon has ______ faces.
• A solid figure with only one vertex is a ______.

• The total number of lateral faces in a pyramid which has eight edges is______.

• The net of a rectangular prism has ______ rectangles.

• If the number of vertices and faces added together in a polyhedron is 14, then the number of edges in that shape is ______.

Answer 13. 

(1) n + 1 .

Explanation: In a pyramid, each side of the polygon contributes to one face, and the number of faces is one more than the number of sides of the polygonal base, i.e. faces = n + 1.

(2) Cone.

(3)  5.

Explanation: Let us calculate the total number of faces using Euler’s formula F + V – E = 2.

Note that in a pyramid, the number of faces = the number of vertices.

Hence Euler’s formula F + V – E = 2 is now F + F – E = 2, 

Given that E = 8,

F + F – 8 = 2

2F – 8 = 2

2F = 8 + 2 = 10

F = 10 / 2 = 5

(4) Six

(5) 12

Explanation: We know that F + V – E = 2 always holds for a polyhedron. 

Given that the sum of the number of faces and vertices = 14, then the number of edges is,

F + v – E = 2 

14 – E = 2

E = 14 – 2 = 12

Hence the total number of edges is 12

Benefits of Solving Important Questions Class 8 Mathematics Chapter 10

Extramarks assist students in laying a solid foundation for all of the subjects covered in their curriculum.. Important Questions Class 8 Mathematics Chapter 10 is extremely helpful for the students preparing for the CBSE examination. The more the students practise these tricky questions, the better they will get at observing the solid and plane shapes and improving their problem-solving skills.

A few of the benefits of referring to Important Questions Class 8 Mathematics Chapter 10 are:

• MCQs, short and medium format questions and answers, and long answer questions are provided with detailed solutions to make students well versed with various questions appearing in the CBSE examination. 
• By rigorously practising these advanced-level questions from the Important Questions Class 8 Chapter 10, students can thoroughly brush up on the concepts, analyse their shortcomings, and overcome them before facing their final school examinations.
• The question and answers to all the Important Questions Class 8 Mathematics Chapter 10 are prepared by our experienced Mathematics faculty per the CBSE syllabus and NCERT guidelines.
• You will likely develop problem-solving and time-management skills by self-monitoring the errors and reducing them by solving more questions on Extramarks.

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