NCERT Solutions for Class 8 Maths Chapter 10, have been prepared in a logical and simple language for fast revisions during the examination. Class 8 CBSE Maths Chapter 10, Exercise 10.3, questions are solved by BYJU’S subject experts using step-by-step solving approach. Th eexercise questions are based on Euler’s formula. For any polyhedron, F + V – E = 2; where ‘F’ stands for the number of faces, V stands for the number of vertices and E stands for the number of edges. Download free NCERT Solutions for Maths Chapter 10 – Visualising Solid Shapes and strengthen your fundamentals.
NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Exercise 10.3
Access Answers to NCERT Class 8 Maths Chapter 10 Visualising Solid Shapes Exercise 10.3 Page number 166
Exercise 10.3 Page No. 166
1. Can a polyhedron have for its faces:
(i) 3 Triangles?
(ii) 4 triangles?
(iii) A square and four triangles?
Solution:
(i) No, such polyhedrons are not possible. A polyhedron should have a minimum of 4 faces.
(ii) Yes, a triangular pyramid has 4 triangular faces.
(iii) Yes, as a square pyramid has a square face and 4 triangular faces.
2. Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid)
Solution:
It is possible only if the number of faces is greater than or equal to 4.
3. Which are prisms among the following:
Solution:
(i) A nail: It is not a prism.
(ii) Unsharpened pencil: It is a prism.
(iii) A table weight: It is not a prism.
(iv) A box: It is a prism.
4. (i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
Solution:
(i) A cylinder can look like a circular prism, a prism with a circular base.
(ii) A cone can be a circular pyramid, a pyramid with a circular base.
5. Is a square prism the same as a cube? Explain.
Solution:
Yes, a square prism can also be a cube. A square prism has a square as its base. However, its height is not necessarily the same as the side of the square. Thus, a square prism can also be a cuboid.
6. Verify Euler’s formula for the given solids.
Solution:
(i) Number of faces, F = 7
Number of edges, E = 15
Number of vertices, V = 10
As per formula, F + V – E = 2
Substitute the values, we have
F + V – E = 7 + 10 – 15
= 2
Hence, verified.
(ii) Here, F = 9, V = 9 and E = 16
Using formula, F+ V – E = 2
F + V – E = 9 + 9 – 16 = 2
Hence, Euler’s formula is verified.
7. Using Euler’s formula, find the unknown:
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
Solution:
Euler’s formula: F + V – E = 2
Where, F = Faces, V = Vertices and E = Edges
(i) F + 6 – 12 = 2
F = 2 + 6
⇒ F = 8
(ii) 5 + V – 9 = 2
V – 4 = 2
⇒ V = 4 + 2
⇒ V = 6
(iii) 20 + 12 – E = 2
32 – E = 2
⇒ E = 32 – 2
⇒ E = 30
8. Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Solution:
From the given data, we have
F = 10
E = 20
V = 15
Every polyhedron satisfies Euler’s formula, which is stated as, F + V – E = 2
For the given polygon,
F + V – E = 10 + 15 – 20 = 25 – 20 = 5, which is not equal to 2.
Therefore, a polyhedron cannot have 10 faces, 20 edges and 15 vertices, as Euler’s formula is not satisfied.
Access Other Exercise Solutions of Class 8 Maths Chapter 10 Visualising Solid Shapes
Exercise 10.1 Solutions : 4 Questions (Short answers)
Exercise 10.2 Solutions : 4 Questions (3 Short answers, 1 Long answer)
NCERT Class 8 Maths Chapter 10 Exercise 10.3, explains about Faces, Edges, and Vertices, and their relationship. The relationship between faces, edges, and vertices is called Euler’s formula, which states that, for any polyhedron, F + V – E = 2”. This relationship is used to verify if the given figure is a polyhedron or not.
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