MCQ Questions for Class 8 Maths Visualising Solid Shapes Quiz 5

Using Euler's formula, find the number of vertices for a given figure with 6 faces and 12 edges.

0%
8
0%
10
0%
12
0%
2

Explanation

Euler's polyhedron formula,

V - E + F = 2

$V - E + F =2$

V

$V$ = number of vertices = ?

E

$E$ = number of edges =

12

$12$

F

$F$ = number of faces =

6

$6$

V - 12 + 6 = 2

$V-12+6=2$

V = 6 + 2

$V = 6+2$

V = 8

$V = 8$
Number of vertices =

8

$8$

Apply Euler's formula for a solid that has 16 faces and 21 edges. How many vertices does it have?

0%
$3$
0%
$5$
0%
$7$
0%
$9$

Explanation

We know that, Euler's polyhedron formula is

V - E + F = 2

$V - E + F =2$
where,

V

$V$ is the number of vertices

E

$E$ is the number of edges

F

$F$ is the number of faces

Here,

E = 16, F = 21

$E=16,\ F=21$

Hence,

V - 21 + 16 = 2

$V-21+16=2$

\Rightarrow V - 5 = 2

$\Rightarrow V -5 = 2$

\Rightarrow V = 7

$\Rightarrow V = 7$

Hence, the solid has

7

$7$ vertices.

A octahedron has _____ faces and 6 vertices with 12 edges. (Use Euler's formula)

0%
4
0%
8
0%
12
0%
24

Explanation

Euler's polyhedron formula,

V - E + F = 2

$V - E + F =2$

V

$V$ = number of vertices =

6

$6$

E

$E$ = number of edges =

12

$12$

F

$F$ = number of faces = ?

6 - 12 + F = 2

$6-12+F=2$

F = 6 + 2

$F = 6+2$

F = 8

$F = 8$
Number of faces =

8

$8$
A octahederon has

8

$8$ faces and

6

$6$ vertices with

12

$12$ edges.

What is the value of F + V - E for a hexagonal prism?

0%
5
0%
1
0%
4
0%
2

Explanation

Euler's polyhedron formula,

V - E + F = 2

$V - E + F =2$
A hexagonal prism has

8

$8$ faces,

F = 8

$F = 8$
A hexagonal prism has

12

$12$ vertices,

V = 12

$V = 12$
A hexagonal prism has

18

$18$ edges,

E = 18

$E = 18$

So,

12 - 18 + 8 = 2

$12 -18+8=2$

How many faces does a solid figure has, if their vertices is

13

$13$ and edges is

24

$24$ ?

0%
$12$
0%
$13$
0%
$14$
0%
$15$

Explanation

Euler's polyhedron formula,

V - E + F = 2

$V - E + F =2$

V

$V$

=

$=$ number of vertices

=

$=$

13

$13$

E

$E$

=

$=$ number of edges

=

$=$

24

$24$

F

$F$

=

$=$ number of faces

= ?

$= ?$
Therefore,

13 - 24 + F = 2

$13-24+F=2$

\Rightarrow F = 11 + 2

$\Rightarrow F = 11+2$

\Rightarrow F = 13

$\Rightarrow F = 13$
Number of faces

=

$=$

13

$13$

Which of the following diagrams represents the front view of the given solid?

A square based pyramid has

5

$5$ faces and

5

$5$ vertices. Find the number of edges.

0%
$6$
0%
$8$
0%
$10$
0%
$12$

Explanation

Euler's polyhedron formula,

V - E + F = 2

$V - E + F =2$

V

$V$

=

$=$ number of vertices

=

$=$

5

$5$

E

$E$

=

$=$ number of edges

= ?

$= ?$

F

$F$

=

$=$ number of faces

=

$=$

5

$5$
Thus

5 - E + 5 = 2

$5-E+5=2$

\Rightarrow E = 10 - 2

$\Rightarrow E = 10-2$

\Rightarrow E = 8

$\Rightarrow E = 8$
Number of edges

=

$=$

8

$8$

Determine whether the given figure is an example of

0%
polyhedron
0%
polygon
0%
triangle
0%
pentagon

A polyhedron whose faces are identical regular polygons is called

0%
convex polyhedron
0%
regular polyhedron
0%
concave polyhedron
0%
irregular polyhedron

In which regular polyhedron, 3 squares meet at each vertex?

The front and side view are same in which figure?

0%
rectangle
0%
square
0%
triangular pyramid
0%
rhombus

Which amongst the following is a polyhedron?

0%
cone
0%
sphere
0%
cube
0%
cylinder

Explanation

$\textbf{Step - 1: Define Polyhedron}$

$\text{A polyhedron is a three dimensional shape with flat polygonal faces, straight edges}$

$\text{ and sharp corners or vertices.}$

$\textbf{Step - 2: Eliminate options}$

$\text{From the above options,}$

$\text{Cones, spheres, and cylinders are non-polyhedrons}$

$\text{Because their sides are not polygons and they have curved surfaces.}$

$\textbf{Hence , option(C) is correct, cube is a polyhedron.}$

In which polyhedron has 6 faces, 8 vertices and 12 edges?

0%
Cube
0%
Sphere
0%
Triangular prism
0%
Cone

Explanation

A cube has

6

$6$ faces,

8

$8$ vertices and

12

$12$ edges.

Flat faces solid is called

0%
polygon
0%
triangle
0%
polyhedron
0%
pyramid

What is the name of the polyhedron?

0%
pyramid
0%
triangular prism
0%
rectangular prism
0%
triangle

Which amongst the following is not a polyhedron?

Explanation

$\textbf{Step - 1: Define Polyhedron}$

$\text{A polyhedron is a three dimensional shape with flat polygonal faces, straight edges}$

$\text{ and sharp corners or vertices}$

$\textbf{Step - 2: Eliminate options}$

$\text{From the above options, all except option (D) is not a polyhedron, because it is a cone.}$

$\textbf{Hence , option(D) is correct, It is not a polyhedron.}$

From the object front view, what will you see?

Which shape is a top view for the given figure?

Explanation

The first option shape is a top view for the given figure because there are only three squares at the topmost surface of the given

3 D

$3D$ figure.

Find out the side view for the given diagram.

How many triangles are there in tetrahedron polyhedron?

0%
4
0%
6
0%
7
0%
9

Explanation

There are

4

$4$ triangles in tetrahedron polyhedron.

In which polyhedron, any plane section is a convex polygon?

0%
convex polyhedron
0%
concave polyhedron
0%
non-convex polyhedron
0%
non-concave polyhedron

Which two figures is an example of convex polyhedron?

0%
figure 1 and figure 2
0%
figure 2 and figure 3
0%
figure 3 and figure 1
0%
figure 2 and figure 4

Identify the convex polyhedron.

Which one of the following is not a convex polyhedron?

The line segment joining any two points on the surface of the polyhedron lies entirely inside or on the polyhedron is called:

0%
convex polyhedron
0%
concave polyhedron
0%
non-convex polyhedron
0%
non-concave polyhedron

Cube is an example of

0%
concave polyhedron
0%
non-convex polyhedron
0%
convex polyhedron
0%
square

From which convex polyhedron 3 triangles meet at each vertex?

0%
octahedron
0%
cube
0%
tetrahedron
0%
dodecahedron

Explanation

In tetrahedron polyhedron

3

$3$ triangles meet at each vertex.

A ______ polyhedron is a figure composed of finitely many planar polygons.

0%
concave
0%
regular
0%
convex
0%
non-concave

The figure is an example of

0%
regular polyhedron
0%
concave polyhedron
0%
irregular polyhedron
0%
convex polyhedron

Which of the following is a convex polyhedron?

CBSE Questions for Class 8 Maths Visualising Solid Shapes Quiz 5 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Visualising Solid Shapes Quiz 5 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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