Mathematics NCERT Grade 7 Chapter 15: Visualising Solid Objects-This chapter will take students through different plane figures and solid shapes.
• The circle, square, rectangle, quadrilateral, and triangle are examples of plane figures; the cube, cuboid, sphere, cylinder, cone, and  pyramid are examples of solid shapes.
• Plane figures are of two-dimensions(2-D) and the solid shapes are of three-dimensions(3-D).
In the first half of the chapter, Faces, Edges and vertices are discussed followed by nets for building 3D shapes.
• Faces: Corners of solid shapes
• Edges: Line segment of the skeleton of solid shapes
• Vertices: Flat surfaces of solid shapes
• A net is a skeleton-outline of a solid that can be folded to make it. The same solid can have several types of nets.
​The topic Drawing Solids on a Flat Surface is explained though different methods:
• Oblique Sketches
• An oblique sketch does not have proportional lengths. Still, it conveys all important aspects of the appearance of the solid.
• Isometric Sketches
• An isometric sketch is drawn on an isometric dot paper. In an isometric sketch of the solid, the measurements kept proportional.
Moving towards the end of the chapter- Visualising Solid Objects, the concept of Viewing Different Sections of a Solid will be discussed.
The different sections of a solid can be obtained by the following methods:
• by Cutting or Slicing
• by Shadow Play
• by Looking at it from Certain Angles to Get Different Views
​Looking at an object from different angles its front-view, side-view and top-view can be obtained that provide a lot of information about the shape observed.

A total of 4 unsolved exercises are given in this chapter. Each exercise is enriched with an adequate number of questions for practice. All the sections of the chapter are explained in great detail.
8 points are listed in the summary of the chapter in the end.

#### Question 1:

Identify the nets which can be used to make cubes (cut out copies of the nets and try it): (i)The given net can be folded as follows. When the faces that are in sky blue colour and in pink colour are folded to make a cube, they will be overlapping each other.

(ii) The given net can be folded as follows. A cube can thus be formed in the above way.

(iii) The given net can be folded as follows. A cube can thus be formed in the above way.

(iv) The given net can be folded as follows. A cube can thus be formed in the above way.

(v) The given net can be folded as follows. When the faces that are in blue colour and in red colour are folded to make a cube, they will be overlapping each other.

(vi) The given net can be folded as follows. A cube can thus be formed in the above way.

#### Question 2:

Dice are cubes with dots on each face. Opposite faces of a die always have a total of seven dots on them. Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box. Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.

(i) The numbers can be inserted as follows so as to make the given net into a net of a dice. It can be observed that the sum of the opposite faces is 7.

(ii)The numbers can be inserted as follows so as to make the given net into a net of a dice. It can be observed that the sum of the opposite faces is 7.

#### Question 3:

Can this be a net for a die? The given net can be folded as follows. It can be observed that the opposite faces of the dice so formed have 2 and 5, 1 and 4, 3 and 6 on them. The sum of the numbers on the opposite faces comes to 7, 5, 9 respectively. However, in case of a dice, the sum of the numbers on the opposite faces should be 7. Hence, this net is not of a dice.

#### Question 4:

Here is an incomplete net for making a cube. Complete it in at least two different ways. Remember that a cube has six faces. How many are there in the net here? (Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.) There are 3 faces in the given net. The given net can be completed as follows.  #### Question 5:

Match the nets with appropriate solids:

 (a) (i) (b) (ii) (c) (iii) (d) (iv) Consider net (i). It can be folded as follows. It is a net of a pyramid. Hence, (d) is the correct matching option.

Consider net (ii). It can be folded as follows. It is a net of a cube. Hence, (a) is the correct matching option.

Consider net (iii). It can be folded as follows. It is a net of a cylinder. Hence, (b) is the correct matching option.

Consider net (iv). It can be folded as follows. It is a net of a cone. Hence, (c) is the correct matching option.

#### Question 1:

Use isometric dot paper and make an isometric sketch for each one of the given shapes:  (i) (ii)  (iii) (iv)

The isometric sketch of these figures can be drawn as follows.  (i) (ii)  (iii) (iv)

#### Question 2:

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

3 isometric sketches of the given cuboid can be drawn as follows.   #### Question 3:

Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.

When three cubes, each of 2 cm edge, are placed side by side, a cuboid with dimensions as 6 cm, 2 cm, and 2 cm will be formed.  Isometric sketch Oblique sketch

#### Question 4:

Make an oblique sketch for each one of the given isometric shapes: The oblique sketch of these figures will be as follows.  #### Question 5:

Give (i) an oblique sketch and (ii) an isometric sketch for each of the following:

(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)

(b) A cube with an edge 4 cm long.

(i) Oblique sketch  (ii) Isometric sketch  The sketch for the cuboid is not unique. The cuboid can also be drawn by taking the length as 3 cm or 2 cm. This will lead to a different view of the same cuboid.

#### Question 1:

What cross-sections do you get when you give a

(i) vertical cut (ii) horizontal cut

to the following solids?

(a) A brick (b) A round apple (c) A die

(d) A circular pipe (e) An ice cream cone

(a) A brick

We can give a vertical cut to a brick in the following way. We can give a horizontal cut to a brick in the following way. (b) A round apple

We can give a vertical cut to a round apple in the following way. We can give a horizontal cut to a round apple in the following way. (c) A die

We can give a vertical cut to a dice in the following way. We can give a horizontal cut to a dice in the following way. (d) A circular pipe

We can give a vertical cut to a circular pipe in the following way. We can give a horizontal cut to a circular pipe in the following way. (e) An ice cream cone

We can give a vertical cut to an ice cream cone in the following way. We can give a horizontal cut to an ice cream cone in the following way. #### Question 1:

A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions). The shapes of the shadows of these figures will be as follows.

(i) A ball The shape of the shadow of a ball will be a circle.

(ii) A cylindrical pipe The shape of the shadow of a circular pipe will be a rectangle.

(iii) A book The shape of the shadow of a book will be a rectangle.

#### Question 2:

Here are the shadows of some 3−D objects, when seen under the lamp of an overhead projector. Identify the solids (s) that match each shadow. (There may be multiple answers for these!) The given shadows can be obtained in case of the following objects.

1. Compact disk

2. A dice

3. Triangular pyramid

4. Note Book

#### Question 3:

Examine if the following are true statements:

(i) The cube can cast a shadow in the shape of a rectangle.

(ii) The cube can cast a shadow in the shape of a hexagon.