From this post important questions with solutions for CBSE Class 8 Maths Chapter 10 - Visualising Solid Shapes prepared by expert Mathematics teachers from the latest edition of CBSE(NCERT) books.

Questions from very important topics are covered by NCERT Exemplar Class 8. You also get the idea about the type of questions and method to answer in your Class 8th examination. Here you can get Class 8 Important Questions Maths based on NCERT Textbook for Class VIII. Maths Class 8 Important Questions are very helpful to score high marks in board exams. Here we have covered Important Questions on Visualising Solid Shapes for Class 8 Maths subject.

In this question paper, questions are covered from the chapter Visualising Solid Shapes and questions are prepared as per NCERT guidelines. Questions are covered from NCERT solutions and NCERT Exemplar.

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Questions:

Generic 2

6 x 2 = 12

Following solids are made by joining cubes. Draw their different views.

Why the following solids are not polyhedron?
(i) A sphere
(ii) A cone
(iii) A cylinder

Find number of faces of a polyhedron, which has 27 edges and 17 vertices.

A polyhedron has 7 faces and 10 vertices. How many edges does the polyhedron have?

The actual width of a classroom is 900 cm. If the scale chosen to make it drawing is 1: 30. Then, what will be the width of the room in the drawing?

Draw two figures for each 1-D, 2-D and 3- D.

Generic 3

5 x 3 = 15

What is Euler's formula? Verify the Euler's formula for a pentagonal prism.

A polyhedron has 40 edges and 30 vertices. Find the number of its faces.

How many vertices does the following solids have?
Octagonal pyramid

10.

Find the number of vertices in a polyhedron which has 30 edges and 12 faces.

11.

Draw a map of your class room using proper scale and symbols for different objects.

Generic 5

2 x 5 = 10

12.

The actual width of a store room is 320 cm. If the scale chosen to make its drawing is 1:4, then find the width of the room in the drawing.

13.

Determine the number of edges, vertices and faces in the following figure. Also, verify your answer.

Multiple Choice Question

5 x 1 = 5

14.

Which of the following is the base of a tetrahedron?

(a)

a square

(b)

a rectangle

(c)

a circle

(d)

a triangle

15.

Which of the following is the number of vertices of sphere?

(a)

(b)

(c)

(d)

16.

Which of the following is the number of vertices of a cone?

(a)

(b)

(c)

(d)

none of these

17.

Side of a square garden is 40 m. If the scale used to draw its picture is 1 cm: 8 m, then the perimeter of the square in the picture is

(a)

15 cm

(b)

25 cm

(c)

20 cm

(d)

32 cm

18.

We have 4 congruent equilateral triangles. What do we need more to make a pyramid?

(a)

An equilateral triangle

(b)

A square with same side length as of triangle

(c)

2 squares with side length same as triangle

(d)

2 equilateral triangles with side length same as triangle

Fill up / 1 Marks

5 x 1 = 5

19.

According to the Euler's formula, we have F + V - E = ________

20.

A ........ has 7 faces.

21.

A flat surface of a three-dimensional figure is a ....... and an is where two faces meet.

22.

The net of a ....... has 6 rectangles.

23.

A pyramid on m sided polygon has ........... faces.

1 Marks

4 x 1 = 4

24.

What is a triangular pyramid? What is a pyramid called if its base is a square?

25.

Write the number of edges.

26.

Write the number of faces.

27.

A polyhedron has 30 edges and 12 vertices. How many faces does it have?

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Answers Key:

Generic 2

6 x 2 = 12

(i)
(ii)

Since, a polyhedron is a solid shape bounded by polygons. However,
(i) a sphere
(ii) a cone and
(iii) a cylinder are not polyhedron because they are not made of polygons, i.e. their faces are not polygons.

Number of faces = 12

For any polyhedron, F + V - E = 2
Here, F = 7, V = 10, E = ?
Using above formula, 7 + 10 - E = 2 ⇒ 17-E = 2 ⇒17 - 2 = E ⇒ E = 15
∴ The polyhedron has 15 edges.

30 cm

Generic 3

5 x 3 = 15

If a polyhedron is having number of faces as F, number of edges as E and the number of vertices as V, then the relationship
F+ V=E+2
is known as Euler's formula. Following figure is a solid pentagonal prism.

It has:
Number of faces (F) = 7
Number of edges (E) = 15
Number of vertices (V) = 10
Substituting the values of F, E and V in the relation,
F+ V=E+2
We have
7 + 10 = 15 + 2
⇒ 17 = 17
which is true, the Euler's formula is verified.

In an octagonal pyramid, there are 9 vertices

10.

For any polyhedron,
F + V - E = 2
Here, F =12, V = ?, E = 30
Using above formula,
12 + V - 30 = 2 ⇒ V - 18 = 2
V = 2 + 18 ⇒ V = 20

11.

A map of a classroom is given below:

Generic 5

2 x 5 = 10

12.

80 cm

13.

The polygonal regions are called faces, hence there are 7 faces. The line segment formed by the intersection of two faces is called edges, hence there are 15 edges. Edges meet at vertices which are points, hence there are 10 vertices.
Verification
The above answer is verified using Euler's Formula.
F + V = E + 2
For the above problem,
F = 7, V = 10 and E = 15
F + V = 7 + 10 = 17
⇒ E + 2 = 15 + 2 = 17
Hence, F + V = E + 2 is verified.

Multiple Choice Question

5 x 1 = 5

14.

(d)
a triangle

15.

(a)
0

16.

(a)
1

17.

18.

(b)
A square with same side length as of triangle

Fill up / 1 Marks

5 x 1 = 5

19.

()
2

20.

()
A pentagonal prism have 7 faces. Since, in a prism, there are two parallel congruent bases.

21.

()
In a 3D-figure, face is the flat surface and where two faces meet, is edge which is a line segment.

22.

()
The net of a rectangular prism has 6 faces as 6 rectangles.

23.

()
Since, a pyramid is a polyhedron that has one base. The base can be any polygon. The other faces are triangles. So, a pyramid on m sided polygon will have (m + 1) faces.

1 Marks

4 x 1 = 4

24.