# RD Sharma Solutions for Class 8 Maths Chapter 19 Visualising Shapes

In Chapter 19, we shall discuss the visualisation of 3D shapes from their plane figures. Students will also learn about the representation of three-dimensional shapes on the plane of the paper. For a better understanding of the concepts, students can solve the exercise-wise problems using the solutions, which are formulated by the subject experts at BYJUâ€™S. Students aiming to secure high marks in the final examination are advised to practise the solutions on a regular basis. RD Sharma Class 8 PDF can be downloaded from the links provided below.

Chapter 19 – Visualising Shapes contains two exercises, and the RD Sharma Class 8 Solutions present in this page provide solutions to the questions given in each exercise. Now, let us have a look at the concepts discussed in this chapter.

• Polyhedra
• Prisms and pyramids
• Platonic solids
• Visualisation of 3D shapes through nets

### Access answers to Maths RD Sharma Solutions for Class 8 Chapter 19 Visualising Shapes

EXERCISE 19.1 PAGE NO: 19.9

1. What is the least number of planes that can enclose a solid? What is the name of the solid?

Solution:

The least number of planes that are required to enclose a solid is 4.

The name of solid is tetrahedron.

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

Solution:

(i) 3 triangles?

No, because a polyhedron is a solid shape bounded by polygons.

(ii) 4 triangles?

Yes, because a tetrahedron as 4 triangles as its faces.

(iii) a square and four triangles?

Yes, because a square pyramid has a square and four triangles as its faces.

3. Is it possible to have a polyhedron with any given number of faces?

Solution:

Yes, if number of faces is four or more.

4. Is a square prism same as a cube?

Solution:

Yes. We know that a square is a three dimensional shape with six rectangular shaped sides, out of which two are squares. Cubes are of rectangular prism length, width and height of same measurement.

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

Solution:

No.

Let us use Eulerâ€™s formula

V + F = E + 2

15 + 10 = 20 + 2

25 â‰  22

Since the given polyhedron is not following Eulerâ€™s formula, therefore it is not possible to have 10 faces, 20 edges and 15 vertices.

6. Verify Eulerâ€™s formula for each of the following polyhedrons:

Solution:

(i) Vertices = 10

Faces = 7

Edges = 15

By using Eulerâ€™s formula

V + F = E + 2

10 + 7 = 15 + 2

17 = 17

Hence verified.

(ii) Vertices = 9

Faces = 9

Edges = 16

By using Eulerâ€™s formula

V + F = E + 2

9 + 9 = 16 + 2

18 = 18

Hence verified.

(iii) Vertices = 14

Faces = 8

Edges = 20

By using Eulerâ€™s formula

V + F = E + 2

14 + 8 = 20 + 2

22 = 22

Hence verified.

(iv) Vertices = 6

Faces = 8

Edges = 12

By using Eulerâ€™s formula

V + F = E + 2

6 + 8 = 12 + 2

14 = 14

Hence verified.

(v) Vertices = 9

Faces = 9

Edges = 16

By using Eulerâ€™s formula

V + F = E + 2

9 + 9 = 16 + 2

18 = 18

Hence verified.

7. Using Eulerâ€™s formula find the unknown:

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

Solution:

(i)

By using Eulerâ€™s formula

V + F = E + 2

6 + F = 12 + 2

F = 14 – 6

F = 8

âˆ´ Number of faces is 8

(ii)

By using Eulerâ€™s formula

V + F = E + 2

V + 5 = 9 + 2

V = 11 – 5

V = 6

âˆ´ Number of vertices is 6

(iii)

By using Eulerâ€™s formula

V + F = E + 2

12 + 20 = E + 2

E = 32 – 2

E = 30

âˆ´ Number of edges is 30

EXERCISE 19.2 PAGE NO: 19.12

1. Which among of the following are nets for a cube?

Solution:

Figure (iv), (v), (vi) are the nets for a cube.

2. Name the polyhedron that can be made by folding each net:

Solution:

(i) From figure (i), a Square pyramid can be made by folding each net.

(ii) From figure (ii), a Triangular prism can be made by folding each net.

(iii) From figure (iii), a Triangular prism can be made by folding each net.

(iv) From figure (iv), a Hexagonal prism can be made by folding each net.

(v) From figure (v), a Hexagonal pyramid can be made by folding each net.

(vi) From figure (vi), a Cuboid can be made by folding each net.

3. Dice are cubes where the numbers on the opposite faces must total 7. Which of the following are dice?

Solution:

Figure (i), is a dice. Since the sum of numbers on opposite faces is 7 (3 + 4 = 7 and 6 + 1 = 7).

4. Draw nets for each of the following polyhedrons:

Solution:

(i) The net pattern for cube is

(ii) The pattern for triangular prism is

(iii) The net pattern for hexagonal prism is

(iv) The net pattern for pentagonal pyramid is

5. Match the following figures:

Solution:

(a)-(iv) Because multiplication of numbers on adjacent faces are equal, where 6Ã—4 = 24 and 4Ã—4 = 16

(b)-(i) Because multiplication of numbers on adjacent faces are equal, where 3Ã—3 = 9 and 8Ã—3 = 24

(c)-(ii) Because multiplication of numbers on adjacent faces are equal, where 6Ã—4 = 24 and 6Ã—3 = 18

(d)-(iii) Because multiplication of numbers on adjacent faces are equal, where 3Ã—3 = 9 and 3Ã—9 = 27