Visualising Solid Shapes Test

Result

Visualising Solid Shapes Test - 3

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Weekly Quiz Competition

Question 1
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Which among the following is a tetrahedron?

A

B

C

D

Solution

Tetrahedron, which is also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices. Option 3 shows a tetrahedron.
Question 2
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Identify the top view of the given shape.

A

B

C

D

Solution

Top view is shown below.

When the above image is viewed from the top, only the shaded faces will be seen. Therefore, figure in option (2) will be the top view of the given figure.
Question 3
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Which among the following is NOT a polyhedron?

A
A brick

B
A spinning top

C
An unsharped pencil

D
A Rubik's cube

Solution

Brick, Rubik's cube and unsharped pencil are polyhedrons. Whereas, a spinning top is conical in shape, therefore, it is not a polyhedron.
Question 4
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If the numbers of vertices and edges of a shape are 16 and 18, respectively, then using Euler's formula, find out the number of faces of the shape.

A
4

B
5

C
6

D
7

Solution

According to Euler's formula: F + V = E + 2
where
F = Number of faces
V = Number of vertices = 16
E = Number of edges = 18
So, F + 16 = 18 + 2
F = 20 - 16 = 4
So, the shape has 4 faces.
Question 5
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Which among the following is the net of a triangular pyramid?

A

B

C

D

Solution

Following is the net of a triangular prism.
Question 6
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How many edges does the following shape have?

A
22

B
18

C
15

D
11

Solution

Number of faces (F) = 8
Number of vertices (V) = 12
Number of edges (E) = ?
Using Eular's formula:
V + F - E = 2
= 12 + 8 - E = 2
E = 18
Therefore, number of edges in the given figure is 18.
Question 7
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Which among the following is true for an octahedron?

A
Faces = 8, Edges = 12, Vertices = 6

B
Faces = 6, Edges = 12, Vertices = 6

C
Faces = 12, Edges = 12, Vertices = 6

D
Faces = 8, Edges = 12, Vertices = 8

Solution

An octahedron has 8 faces, 12 edges and 6 vertices.
Question 8
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Which among the following is the net of a pentagonal prism?

A

B

C

D

Solution

Among the given options, following is the net of a pentagonal prism.
Question 9
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The number of vertices in a rectangular pyramid is ________.

A
5

B
6

C
8

D
9

Solution

A rectangular pyramid is a three-dimensional object with a rectangular base and a triangular face along each side of the base. Number of vertices in this shape is 5.
Question 10
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Identify the front view of the following object:

A

B

C

D

Solution

The front view of the given object is:
Question 11
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Which among the given options is the side view of the following shape?

A

B

C

D

Solution

The side view of the given figure is mentioned below.

Hence, option 2 is correct.
Question 12
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Solid not having line segments as its edges is

A
Tetrahedron

B
Cylinder

C
Octahedron

D
Polyhedron

Solution

Solid not having line segments as its edges is cylinder.
All polyhedrons (tetrahedron and octahedron) are made up of line segments.
Question 13
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If a polyhedron has 12 edges and 8 faces, then how many vertices does that polyhedron have?

A
4

B
5

C
6

D
7

Solution

Number of faces (F) = 8
Number of vertices (V) = ?
Number of edges (E) = 12
Using Euler's formula:
F + V - E = 2
So, 8 + V - 12 = 2
V - 4 = 2
V = 2 + 4 = 6
So, it has 6 vertices and the polyhedron is octahedron.
Question 14
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There is a structure in Egypt in the shape of a square pyramid. How many vertices does that structure have?

A
5

B
4

C
3

D
2

Solution

A square pyramid is a pyramid with a square base.
It has 5 vertices.
Question 15
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Which among the following will form a polyhedron?

A
1 square and 3 triangles

B
1 triangle and 2 squares

C
1 pentagon and 5 triangles

D
2 square and 2 triangle

Solution

A polyhedron contains more than four polygonal faces. So, among the given options, 1 pentagon and 5 triangles together will form a polyhedron.

Question 16

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Using Euler's formula, find the values of M, N, O and P in the given table:

	(I)	(II)	(III)	(IV)
Faces	10	8	O	7
Vertices	M	6	8	P
Edges	24	N	12	12

M - 12, N - 14, O - 7, P - 6

M - 13, N - 15, O - 3, P - 8

M - 16, N - 12, O - 6, P - 7

M - 14, N - 11, O -5, P - 8

Solution

According to Euler's formula:
F + V = E + 2
where
F = Number of faces
V = Number of vertices
E = Number of edges

Now, in (I):
F = 10, E = 24
So, 10 + V = 24 + 2
V = 26 - 10 = 16
Therefore, it has 16 vertices.

In (II):
F = 8, V = 6
8 + 6 = E + 2
14 - 2 = E
E = 12
Therefore, it has 12 edges.

In (III):
V = 8, E = 12
F + 8 = 12 + 2
F = 14 - 8 = 6
Therefore, it has 6 faces.

In (IV):
F = 7, E = 12
7 + V = 12 + 2
V = 14 - 7 = 7
Therefore, it has 7 vertices.

So, M = 16
N = 12
O = 6
P = 7

Question 17
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Match the shapes in Column I with their respective nets (not drawn to scale) in Column II:

A
A - (iv), B - (i), C - (iii), D - (ii)

B
A - (i), B - (ii), C - (iv), D - (iii)

C
A - (iv), B - (i), C - (ii), D - (iii)

D
A - (iv), B - (iii), C - (i), D - (ii)

Solution

Option 1 is correct.

32 = 8 x 4, 16 = 8 x 2, 8 = 4 x 2

64 = 8 x 8, 40 = 8 x 5

12 = 6 x 2, 4 = 2 x 2

28 = 7 x 4, 16 = 4 x 4
Question 18
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Select the incorrect match from the following:

A
A

B
B

C
C

D
D

Solution

According to Euler's formula:
F + V = E + 2
where
F = Number of faces
V = Number of vertices
E = Number of edges

In case of figure C:
Faces = 8
Vertices = 12
Edges = 18 (not 15)
Question 19
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Fill in the blanks:

(1) All the sides of a cube are ___(A)___ to one another.

(2) A pentagonal pyramid has (B) faces.

(C) The net can be made to form a ___(C)___.
(D) A hexagonal pyramid has (D) vertices.

A
A - equal, B - 6, C - triangular prism , D - 7

B
A - parallel, B - 4, C - rectangular prism, D - 6

C
A - equal, B - 5, C - triangular prism, D - 7

D
A - equal, B - 6, C - triangular prism, D - 8

Solution

(A) All the sides of a cube are equal to one another.
(B)

As seen in the above figure, a pentagonal pyramid has 6 faces.

(C) The given figure is a net of a triangular prism.

(D)

A hexagonal pyramid has 7 vertices.
Question 20
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Mark 'T' for True and 'F' for False:

(1) Hexagonal Pyramid has 6 hexagons.
(2) The base and the top of a cylinder have different areas.
(3) A cylinder is a prism.
(4) If the numbers of faces and edges in a shape are 5 and 8, respectively, then the number of vertices is 5.

A
(1) - F, (2) - T, (3) - F (4) - T

B
(1) - T, (2) - T, (3) - T, (4) - T

C
(1) - F, (2) - F, (3) - F, (4) - T

D
(1) - F, (2) - F, (3) - T, (4) - F

Solution

(1) Hexagonal Pyramid has 6 hexagons. - False
It has only 1 hexagon.

(2) The base and the top of a cylinder are different. - False
The base and the top of a cylinder have the same area.

(3) A cylinder is a prism. - False
A prism is a polyhedron, which means all faces are flat. A cylinder is not a prism, because it has curved sides.
(4) If the numbers of faces and edges in a shape are 5 and 8, respectively, then the number of vertices is 5. - True
According to Euler's formula, F + V = E + 2
Now, F = 5 , E = 8
5 + V = 8 + 2
V = 10 - 5 = 5