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.