Chapter 10 Visualising Solid Shapes

Very Short Answer Type

Question 1.
Draw any four 3-dimensional figures.
Solution:
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q1

Question 2.
Verify Euler’s formula for a right triangular prism.
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q2
Solution:
Number of vertices (V) = 6
Number of faces (F) = 5
and number of edges (E) = 9
Euler’s formula:
V + F – E = 2
⇒ 6 + 5 – 9 = 2
⇒ 2 = 2
Hence, the formula is verified.

Question 3.
Find the number of vertices of hexagonal prisms.
Solution:
Number of vertices = 2 × Number of sides = 2 × 6 = 12

Question 4.
Verify whether a polyhedron can have 10 faces, 20 edges and 15 vertices.
Solution:
We have
Number of faces F = 10
Number of edges E = 20
and number of vertices V = 15
Euler’s formula:
V + F – E = 2
⇒ 15 + 10 – 20 = 2
⇒ 5 ≠ 2
Hence, it is not possible to have a polyhedron satisfying the above data.

Question 5.
If F = 18 and V = 10, then find the value of E in Euler’s formula.
Solution:
We know that
V + F – E = 2
⇒ 10 + 18 – E = 2
⇒ 28 – E = 2
⇒ E = 28 – 2 = 26
Hence, the required value of E = 26

Question 6.
Draw the front, side and top views of the following 3-D figures.
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q6
Solution:
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q6.1

Question 7.
Draw the nets of the following polyhedrons.
(i) Cuboid
(ii) Triangular prism with a base equilateral triangle.
(iii) Square pyramid.
Solution:
(i) The net pattern of cuboid
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q7
(ii) The net pattern of a triangular prism
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q7.1
(iii) Net pattern of square pyramid
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q7.2

Question 8.
The given net is made up of two equilateral triangles and three rectangles.
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q8
(i) Name the solid it represents.
(ii) Find the number of faces, edges and vertices.
Solution:
(i) The given figure represents the net prims of the triangular prism
(ii) Number of faces = 5
Number of edges = 9
Number of vertices = 6

Short Answer Type

Question 9.
Match the following:
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q9
Solution:
(a) → (vi)
(b) → (v)
(c) → (ii)
(d) → (i)
(e) → (iii)
(f) → (v)

Question 10.
Using Euler’s formula, fill in the blanks:

Faces

Vertices

Edges

(a)

6

8

(b)

10

15

(c)

4

6

(d)

5

6

(e)

8

12

(f)

7

7

Solution:
(a) F + V – E = 2
⇒ 6 + 8 – E = 2
⇒ 14 – E = 2
⇒ E = 14 – 2 = 12

(b) F + V – E = 2
⇒ F + 10 – 15 = 2
⇒ F – 5 = 2
⇒ F = 2 + 5 = 7

(c) F + V – E = 2
⇒ 4 + V – 6 = 2
⇒ V – 2 = 2
⇒ V = 2 + 2 = 4

(d) F +V – E = 2
⇒ 5 + 6 – E = 2
⇒ 11 – E = 2
⇒ E = 11 – 2 = 9

(e) F + V – E = 2
⇒ 8 + 12 – E = 2
⇒ 20 – E = 2
⇒ E = 20 – 2 = 18

(f) F + V – E = 2
⇒ 7 + 7 – E = 2
⇒ 14 – E = 2
⇒ E = 14 – 2 = 12
Hence (a) → 12, (b) → 7, (c) → 4, (d) → 9, (e) → 18, (f) → 12

Question 11.
Name the solids that have:
(i) 4 faces
(ii) 8 triangular faces
(iii) 6 faces
(iv) 1 curved surface
(v) 5 faces and 5 vertices
(vi) 6 rectangular faces and 2 hexagonal faces
Solution:
(i) Tetrahedron
(ii) Regular octahedron
(iii) Cube and cuboid
(iv) Cylinder
(v) Square and a rectangular pyramid
(vi) Hexagonal prism

Question 12.
Complete the table:

Solid

F

V

E

F + V

E + 2

Cuboid

Triangular
pyramid

Triangular prism

Pyramid with square base

Prism with square base

Solution:

Solid

F

V

E

F + V

E + 2

Cuboid

6

8

12

14

14

Triangular
pyramid

4

4

6

8

8

Triangular
prism

5

6

9

11

11

Pyramid with square base

5

5

8

10

10

Prism with square base

6

8

12

14

14

Question 13.
Use isometric dot paper to sketch a rectangular prism with length 4 units, height 2 units and width 3 units. (NCERT Exemplar)
Solution:
Steps:
1. Draw a parallelogram with sides 4 units and 3 units. This is the top of the prism (Fig. 1).
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q13
2. Start at one vertex. Draw a line passing through two dots. Repeat for the other three vertices. Draw the hidden edges as a dashed line (Fig. 2).
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q13.1
3. Connect the ends of the lines to complete the prism (Fig. 3).
Visualising Solid Shapes NCERT Extra Questions for Class 8 Maths Q13.2

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Chapter 10 Visualising Solid Shapes