NCERT Solutions for Class 8 Maths Chapter 10: Visualising Solid Shapes - Exercise 10.3

Exercise 10.3

Refer to pages 14-17 for exercise 10.3 in the PDF

1. Can a polyhedron have for its faces

(i) 3 triangles? 

Ans: A polyhedron with 3 triangular faces is not possible. Because the edges of a polyhedron must meet at vertices. A polyhedron has a minimum of 4 faces.

(ii) 4 triangles?

Ans: Yes, a triangular pyramid has 4 triangular faces. Because all the eight edges meet at the vertices

(iii) a square and four triangles?

Ans: Yes, a square pyramid has a square face and 4 triangular faces. Because all the eight edges meet at the vertices.

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

Ans: A polyhedron has a minimum of 4 faces.

3. Which are prisms among the following?

(i) A nail

Ans: It is not a prism.It is not a polyhedron as it has a curved surface. 

(ii) Unsharpened pencil 

Ans: It is a prism.

(iii) A table weight

(Image Will Be Updated Soon)

Ans: It is not a prism. It is a pyramid.

(iv) A box

Ans: It is a prism.

4. (i) How are prisms and cylinders alike?

Ans: A cylinder is a prism that has a circle as its base. It is called a circular prism.

(ii) How are pyramids and cones alike?

Ans: A cone is a pyramid that has a circle as its base. So it can be called a circular pyramid.

5. Is a square prism the same as a cube? Explain.

Ans: A square prism has a square as its base. However, its height is not necessarily sameas the side of the square. Thus, a square prism can also be a cuboid.

6. Verify Euler’s formula for these solids.

(i)

Ans: By Euler’s formula, we have

\[F + V - E = 2\]

Here \[F\], \[V\] and \[E\] are the number of faces ,vertices and edges respectively.

In first figure,

Number of faces,\[F = 7\]

Number of vertices,\[V = 10\]

Number of edges ,\[E = 15\]

We have, \[F + V - E = 7 + 10 -15\]\[ = 17 - 15 = 2\]

Hence, Euler’s formula is verified.

(ii)

Ans: Number of faces \[F = 9\]

Number of vertices, \[V = 9\]

Number of edges, \[E = 16\]

We have, \[F + V - E = 9 + 9 -16\]\[ = 18 - 16 = 2\]

Hence, Euler’s formula is verified.

7. Using Euler’s formula, find the unknown.

Ans: By Euler’s formula, we have

\[F + V - E = 2\]

(i) Ans: Number of vertices, \[V = 5\]

Number of edges, \[E = 12\]

Then substitute the given values in Euler’s formula

\[F + 6 - 12 = 2\]

\[F - 6 = 2\]

\[F = 8\]

(ii) Ans: Number of faces, \[F = 5\]

Number of edges, \[E = 9\]

Then substitute the given values in Euler’s formula

\[5 + V - 9 = 2\]

\[V - 4 = 2\]

\[V = 6\]

(iii) Ans: Number of faces \[F = 20\]

Number of vertices, \[V = 12\]

Then substitute the given values in Euler’s formula

\[20 + 12 - E = 2\]

\[32 - E = 2\]

\[E = 30\]

Thus, the table can be completed as

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

Ans: Number of faces, \[F = 10\]

Number of edges, \[E = 20\]

Number of vertices, \[V = 15\]

Polyhedron will satisfy the Euler’s Formula\[F + V - E = 2\]

For the given polygon,

\[F + V - E = 10 + 15 - 20\]

\[ = 25 - 20 = 5 \ne 2\]It is not satisfying Euler’s formula, such a polyhedron is not possible.

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

Opting for the NCERT solutions for Ex 10.3 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 10.3 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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