NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3

# NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3

## NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3 are the part of NCERT Solutions for Class 8 Maths. Here you can find the NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3.

### Ex 10.3 Class 8 Maths Question 1.

Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?

Solution:
(i) No, because polyhedron must have edges meeting at vertices which are points.
(ii) Yes, because all the edges are meeting at the vertices. For example, a tetrahedron.

(iii) Yes, because all the eight edges meet at the vertices. For example, a square pyramid

### Ex 10.3 Class 8 Maths Question 2.

Is it possible to have a polyhedron with any given number of faces?
(Hint: Think of a pyramid)

Solution:

Yes, it is possible if the number of faces is greater than or equal to 4.
For example: Tetrahedron or triangular pyramid which has 4 faces.

### Ex 10.3 Class 8 Maths Question 3.

Which are prisms among the following?

Solution:
(ii) Unsharpened pencil and (iv) A box are the prisms.

### Ex 10.3 Class 8 Maths Question 4.

(i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?

Solution:
(i) If the number of sides of the base in a prism is increased to a certain extent, then the prism will take the shape of a cylinder.
(ii) If the number of sides of the base in a pyramid is increased to a certain extent, then the pyramid will take the shape of a cone.

### Ex 10.3 Class 8 Maths Question 5.

Is a square prism same as a cube? Explain.

Solution:
A cube is a square prism but every square prism cannot be cube. A square prism may be a cuboid also.

### Ex 10.3 Class 8 Maths Question 6.

Verify Euler’s formula for these solids.

Solution:
(i) Faces = 7
Sides = 15
Vertices = 10
Verification of Euler’s formula: F + V – E = 2
7 + 10 – 15 = 2
2 = 2
Hence, Euler’s formula is verified.

(ii) Faces = 9
Sides = 16
Vertices = 9
Verification of Euler’s formula: F + V – E = 2
9 + 9 – 16 = 2
2 = 2
Hence, Euler’s formula is verified.

### Ex 10.3 Class 8 Maths Question 7.

Using Euler’s formula find the unknown.

 Faces ? 5 20 Vertices 6 ? 12 Edges 12 9 ?

Solution:

Using Euler’s Formula: F + V – E = 2

 Faces 8 5 20 Vertices 6 6 12 Edges 12 9 30

### Ex 10.3 Class 8 Maths Question 8.

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Solution:
Here, faces (F) = 10, edges (E) = 20, vertices (V) = 15
According to Euler’s Formula:
F + V – E = 2
10 + 15 – 20 = 25 – 20
5 ≠ 2
Therefore, a polyhedron do not have 10 faces, 20 edges and 15 vertices.

You can also like these:

NCERT Solutions for Maths Class 9

NCERT Solutions for Maths Class 10

NCERT Solutions for Maths Class 11

NCERT Solutions for Maths Class 12