Visualising Solid Shapes Test

Result

Visualising Solid Shapes Test - 2

Score
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Question 1
1 / -0

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 2
1 / -0

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 3
1 / -0

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 4
1 / -0

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

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

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

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

D
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 5
1 / -0

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