# Free Visualising Solid Shapes Subjective Test 01 Practice Test - 7th grade

What shape is made by joining 4 triangles together?  [1 MARK]

#### SOLUTION

Solution :

This shape has a triangular base, and the sides are made from 3 triangles which meet at the top. The resultant shape is a pyramid.

(i) How are cylinders formed from a prism?

(ii) How are cones formed from pyramids?

[2 MARKS]

#### SOLUTION

Solution :

Explanation: 1 Mark each

(i) A prism becomes a cylinder when the number of sides increases.

(ii) When the number of sides of the pyramid increases, it becomes a cone.

Is cuboid a prism? State the key feature of a prism. [2 MARKS]

#### SOLUTION

Solution :

Key feature: 1 Mark

A cuboid has 6 faces which are all rectangles.

Cuboid is a rectangular prism.

The key feature of a prism is that it has a rectangular cross-section along its length. The cuboid also has a rectangular cross-section, which makes it a prism.

Give some examples of prisms?  [2 MARKS]

#### SOLUTION

Solution :

Examples: 0.5 Marks each

Few examples of prisms are:

a) Triangular prism

b) Hexagonal prism

c) Cuboid

d) Cube

What is meant by Oblique Sketches and Isometric Sheets?  [2 MARKS]

#### SOLUTION

Solution :

Definition: 1 Mark each

An Oblique sketch does not have proportional lengths, still, it conveys all important aspects of the appearance of the solid.

An Isometric Sketch is drawn on an isometric dot paper. In an isometric sketch of the solid, the measurements are kept proportional.

Define the following terms: [3 MARKS]

a. Vertices

b. Edges

c. Faces

#### SOLUTION

Solution :

Definition: 1 Mark each

a. A vertex (plural: vertices) is a point where two or more straight lines meet. E.g. The 8 corners of the cube are its vertices.

b. An edge is a line segment that joins two vertices. E.g. The 12 line segments that form the skeleton of the cube are its edges.

c. A face is any of the individual surfaces of a solid object. E.g. The 6 flat square surfaces of the cube are its faces.

The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid. [3 MARKS]

#### SOLUTION

Solution :

Each drawing: 1 Mark

The three isometric sketches of the given cuboid can be drawn as follows:

If we have a polyhedron, which of the following is true about its faces? Explain. [3 MARKS]

(i) It has 3 triangular faces.

(ii) It has 4 triangular faces.

(iii) It has 1 square and 4 triangular faces.

#### SOLUTION

Solution :

Solution: 1 Mark each

A polyhedron is a solid with flat polygonal faces, straight edges and vertices.

(i) This is not true. The minimum number of faces a polyhedron can have is 4. Hence 3 triangles cannot be the faces of a polyhedron.

(ii) This is true. A polyhedron with 4 triangles as faces is known as a regular tetrahedron.

(iii) This is true. A polyhedron with 1 square and 4 triangular faces is known as a square pyramid.

(a) Two cubes of dimensions 2 cm×2 cm×2 cm are placed side by side. What is the length of the resulting cuboid?

(b) How many faces, vertices and edges does a triangular prism have?

[3 MARKS]

#### SOLUTION

Solution :

Each part: 1.5 Marks

(a) As it is clearly evident from the figure, when we place two cubes side by side, their length gets added, but there is no change in the other dimensions.

Length = 2 + 2 = 4 cm

Height = 2 cm

(b)

Number of Faces = 5

Number of Vertices = 6

Number of Edges = 9

Using Euler's formula, find the unknown. [4 MARKS]

Faces?520Vertices6?12Edges129?

#### SOLUTION

Solution :

Formula: 1 Mark
Application: 1 Mark each

Euler's formula = F + V - E = 2

F + 6 - 12 = 2

F - 6 = 2

F = 8

5 + V - 9 = 2

V - 4 = 2

V = 6

20 + 12 - E = 2

32 - 2 = E

E = 30

Verify Euler's formula for the following solids.  [4 MARKS]

#### SOLUTION

Solution :

Each part: 2 Marks

(i) Faces = 7, Vertices = 10, Edges = 15

By Euler's Formula, F + V - E = 2

7 + 10 - 15 = 2

17 - 15 = 2

Therefore, Euler's Theorem is verified.

(ii) Faces = 9, Vertices = 9, Edges = 16

By Euler's Formula, F + V - E = 2

9 + 9 - 16 = 2

18 - 16 = 2

Therefore, Euler's Theorem is verified.

(i) Identify the views of the given blocks.  [4 MARKS]

(ii) Identify the views of the given image.

#### SOLUTION

Solution :

Each part: 2 Marks

(i)

(a) Left view

(b) Top view

(c) Right view

(d) Front view

(ii)

(a) Front View

(b) Top View

(c) Side View

Find whether the following table satisfies the EULER'S formula or not. [4 MARKS]

No. of FacesNo. of VerticesNo. of Edges346381246123203051230

#### SOLUTION

Solution :

Formula: 1.5 Marks
Application: 0.5 Mark each

Euler’s Formula:
Faces + Vertices – Edges = 2

1)  3 + 4 - 6 = 1

1   2

2) 3 + 8 -12 = -1

1   2

3) 4 + 6 - 12 = -2

-2 2

4) 3 + 20 - 30 = -7

-7 2

5)  5 + 12 - 30 = -13

-13 2

(a) How many bags of sugar are there in this box?

(b) How many extra bags can be filled in this box?

[4 MARKS]

#### SOLUTION

Solution : Each part: 2 Marks

(a) There are 3 vertical columns of sugar bags in this box.

The first column has 9 bags of which 5 can be seen and the other 4 are completely hidden.

The second column has 6 bags of which 4 can be seen, and similarly, the third column has 3 bags.

So, the total number of bags = 9 + 6 + 3 = 18.

(b) Now, in the second column, we can see that there is space for 3 more bags and the third column has space for 6 more bags.

The remaining space can be filled with 2 more vertical columns, each having 9 bags.

So, there is a space in the box for 3+6+(9×2)=9+18=27 more bags.

Using Euler's formula complete the following table.
[4 MARKS]
FacesVerticesEdges1010?8?1868??5812?19

#### SOLUTION

Solution : Formula: 1 Mark

Euler's formula: F + V - E = 2

1) 10 + 10 - E = 2

E = 20 - 2

E = 18

2) 8 + V - 18 = 2

V = 10 + 2

V = 12

3) 6 + 8 - E = 2

E = 14 - 2

E = 12

4) F + 5 - 8 = 2

F = 2 + 3

F = 5

5) 12 + V - 19 = 2

V = 2 + 7

V = 9