Visualising Solid Shapes

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NCERT Solutions for Chapter 15 Visualising Solid Shapes Class 7 Maths

Book Solutions

1

Identify the nets which can be used to make cubes (cut out copies of the nets and try it)
(i) 
(ii) 

(iii) 
(iv) 
(v) 
(vi) 

Answer

Cube’s nets are (ii), (iii), (iv) and (vi).
Exercise 15.1 Page Number 281

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.

Answer

(i) 
(ii) 

Exercise 15.1 Page Number 281

3

Can this be a net for a die? Explain your answer.

Answer

No, this cannot be a net for a die.
Because one pair of opposite faces will have 1 and 4 on them and another pair of opposite faces will have 3 and 6 on them whose total is not equal to 7.

Exercise 15.1 Page Number 281

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 faces are there in the net here? (Give two separate diagrams. If you like, you may use a squared sheet for easy manipulation.)

Answer

There three faces are given:

Exercise 15.1 Page Number 282

5

Match the nets with appropriate solids:

(b)      (ii) 
(c)         (iii) 
(d)                (iv) 

Answer

Solids Their nets:
(a) (ii) 
(b)     (iii) 
(c)              (iv) 
(d)     (i) 

Exercise 15.1 Page Number 282

1

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

Answer

(i) 
(ii) 
(iii) 
(iv) 
Exercise 15.2 Page Number 285

2

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

Answer

The dimensions of given cuboid are 5 cm, 3 cm and 2 cm:

Three different isometric sketches are:
Exercise 15.2 Page Number 285

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.

Answer

Oblique sketch:

Isometric sketch

Exercise 15.2 Page Number 285

4

Make an oblique sketch for each one of the given isometric shapes:
(a) 
(b)

Answer

Oblique sketches:
(a) 
(b) 
Exercise 15.2 Page Number 285

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.

Answer

(a) A cuboid of dimension 5 cm, 3 cm and 2 cm.
(i) Oblique sketch (ii) Isometric sketch

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

(ii) Isometric sketch

Exercise 15.2 Page Number 286

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.

Answer

S.No.

Name of article

Figure

Vertical cut

Horizontal cut

(a)

A brick

 

 

 

(b)

A round apple

 

 

 

(c)

A die

 

 

 

(d)

 A circular pipe

 

 

 

(e)

An ice-cream cone

 

 

 

Exercise 15.3 Page Number 288

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).

Answer

S.No.

Object

Shadow

Shape’s name

(i)

A ball



Circle

(ii)

A cylindrical pipe




Line

(iii)

A book



Rectangle

Exercise 15.4 Page Number 289

2

Here are the shadows of some 3-D objects, when seen under the lamp of the overhead projector. Identify the solid (s) that match each shadow.
(There may be multiple answers for these!)
A circle, A square, A triangle, A rectangle
(i) 
(ii) 
(iii) 
(iv) 

Answer

S. No.

Shadow

Shape’s Name

3-D objects

(i)



Circle

Chapatti, Football, Disc, Plate etc.

(ii)



Square

Die, Square paper sheet, cubical magic box, Chalk box etc.

(iii)



Triangle

Ice-cream cone, Birthday cap, etc.

(iv)



Rectangle

Geometry box, Book, Table etc.

Exercise 15.4 Page Number 289

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.

Answer

(i) True
(ii) False
Exercise 15.4 Page Number 290

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