The DAV Maths Book Class 8 Solutions Pdf and **DAV Class 8 Maths Chapter 14 Worksheet 8** Solutions of Mensuration offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 14 WS 8 Solutions

Question 1.

How many faces do the following polyhedrons have?

(i) Triangular prism

(ii) Rectangular pyramid

(iii) Triangular pyramid

Solution:

(i) Triangular prism has 5 faces.

(ii) The rectangular pyramid has 5 faces.

(iii) Triangular pyramid has 4 faces.

Question 2.

How many vertices and edges do the following polyhedrons have?

(i) Square pyramid

(ii) Triangular prism

Solution:

(i) A square pyramid has 5 vertices and 8 edges.

(ii) A triangular pyramid has 6 vertices and 9 edges.

Question 3.

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

Solution:

In a square prism, all the faces are the same.

In a cube, all the faces are also the same.

So, both the polyhedrons are similar to each other.

Question 4.

Verify Euler’s formula for the given figures.

Solution:

(i) Here F = 6, V = 8 and E = 12

According to Euler’s formula,

F + V – E = 2

⇒ 6 + 8 – 12 = 2

⇒ 2 = 2

Hence verified.

(ii) Here F = 9, V = 9 and E = 16

According to Euler’s formula,

F + V – E = 2

⇒ 9 + 9 – 16 = 2

⇒ 2 = 2

Hence verified.

(iii) Here F = 6, V = 8 and E = 12

According to Euler’s formula,

F + V – E = 2

⇒ 6 + 8 – 12 = 2

⇒ 2 = 2

Hence verified.

(iv) Here, F = 5, V = 5, E = 8

According to Euler’s formula

F + V – E = 2

⇒ 5 + 5 – 8 = 2

⇒ 2 = 2

Hence verified.

Question 5.

Using Euler’s formula, find the unknown.

Solution:

(i) For I polyhedron,

F = 8, V = ?, E = 12

From Euler’s formula,

F + V – E = 2

⇒ 8 + V – 12 = 2

⇒ V – 4 = 2

⇒ V = 4 + 2 = 6

(ii) For II polyhedron,

F = ?, V = 6 and E = 9

From Euler’s formula,

F + V – E = 2

⇒ F + 6 – 9 = 2

⇒ F – 3 = 2

⇒ F = 2 + 3 = 5

(iii) For III polyhedron,

F = 10, V = 12, E = ?

From Euler’s formula

F + V – E = 2

⇒ 10 + 12 – E = 2

⇒ 22 – E = 2

⇒ E = 22 + 2 = 24

Question 6.

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

Solution:

Here, F = 10, V = 15 and E = 20

From Euler’s formula,

F + V – E = 2

⇒ 10 + 15 – 20 = 2

⇒ 5 ≠ 2

Hence, no polyhedron is possible with the given measurement.