## RD Sharma Class 8 Solutions Chapter 19 Visualising Shapes Ex 19.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 19 Visualising Shapes Ex 19.1

**Other Exercises**

- RD Sharma Class 8 Solutions Chapter 19 Visualising Shapes Ex 19.1
- RD Sharma Class 8 Solutions Chapter 19 Visualising Shapes Ex 19.2

**Question 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 can enclose a solid is called a Tetrahedron.

**Question 2.**

**Can a polyhedron have for its faces :**

**(i) three triangles ?**

**(ii) four triangles ?**

**(iii) a square and four triangles ?**

**Solution:**

(i) No, polyhedron has three faces.

(ii) Yes, tetrahedron has four triangles as its faces.

(iii) Yes, a square pyramid has a square as its base and four triangles as its faces.

**Question 3.**

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

**Solution:**

Yes, it is possible if the number of faces is 4 or more.

**Question 4.**

**Is a square prism same as a cube ?**

**Solution:**

Yes, a square prism is a cube.

**Question 5.**

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

**Solution:**

No, it is not possible as By Euler’s formula

F + V = E + 2

⇒ 10 + 15 = 20 + 2

⇒ 25 = 22

Which is not possible

**Question 6.**

**Verify Euler’s formula for each of the following polyhedrons :**

**Solution:**

(i) In this polyhedron,

Number of faces (F) = 7

Number of edges (E) = 15

Number of vertices (V) = 10

According to Euler’s formula,

F + V = E + 2

⇒ 7 + 10 = 15 + 2

⇒ 17 = 17

Which is true.

(ii) In this polyhedron,

Number of faces (F) = 9

Number of edges (E) = 16

Number of vertices (V) = 9

According to Euler’s formula,

F + V = E + 2

⇒ 9 + 9 = 16 + 2

⇒ 18 = 18

Which is true.

(iii) In this polyhedron,

Number of faces (F) = 9

Number of edges (E) =18

Number of vertices (V) = 11

According to Euler’s formula,

F + V = E + 2

⇒ 9 + 11 = 18 + 2

⇒ 20 = 20

Which is true.

(iv) In this polyhedron,

Number of faces (F) = 5

Number of edges (E) = 8

Number of vertices (V) = 5

According to Euler’s formula,

F + V = E + 2

⇒ 5 + 5 = 8 + 2

⇒ 10 = 10

Which is true.

(v) In the given polyhedron,

Number of faces (F) = 9

Number of edges (E) = 16

Number of vertices (V) = 9

According to Euler’s formula,

F + V = E + 2

⇒ 9 + 9 = 16 + 2

⇒ 18 = 18

Which is true.

**Question 7.**

**Using Euler’s formula, find the unknown:**

**Solution:**

We know that Euler’s formula is

F + V = E + 2

(i) F + 6 = 12 + 2

⇒ F + 6 = 14

⇒ F = 14 – 6 = 8

Faces = 8

(ii) F + V = E + 2

⇒ 5 + V = 9 + 2

⇒ 5 + V = 11

⇒ V = 11 – 5 = 6

Vertices = 6

(iii) F + V = E + 2

⇒ 20 + 12 = E + 2

⇒ 32 = E + 2

⇒ E = 32 – 2 = 30

Edges = 30

Hope given RD Sharma Class 8 Solutions Chapter 19 Visualising Shapes Ex 19.1 are helpful to complete your math homework.

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