Visualising Solid Shapes| NCERT Solutions| Class 7

NCERT Solutions of Chapter: Visualising Solid Shapes. NCERT Solutions along with worksheets and notes for Class 7.

 

Exercise 15.1

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

 

Diagram of Question 1 of Exercise 15.1 of NCERT Chapter Visualising Solid Shapes                       

i                                                                             ii

                                                   Diagram of Question 1(iv) of Exercise 15.1 of NCERT Chapter Visualising Solid Shapes

iii                                                                                       iv

                                   

v                                                                                      vi

 

Ans-

Nets which can be used to make cubes are given below:

(We can get our cube by folding the nets in the order of numbers on it)

 

ii

iii

iv

vi

 

(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.

 

Diagram of Question 2 of Exercise 15.1 of NCERT Chapter Visualising Solid Shapes                             

i                                                                        ii

Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.

Ans-

Suitable numbers in the blanks are showing below:-

i

 

ii

 

 

(3) Can this be a net for a die?

Explain your answer.

Diagram of Question 3 of Exercise 15.1 of NCERT Chapter Visualising Solid ShapesVisualising solid shapes,A 3,Ex - 15.1,NCERT

(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)

Diagram of Question 4 of Exercise 15.1 of NCERT Chapter Visualising Solid Shapes

Ans-

Required diagram of making a cube are given below:

(i)

 

(ii)

 

 

(5) Match the nets with appropriate solids:

Diagram of Question 5 of Exercise 15.1 of NCERT Chapter Visualising Solid Shapes

Ans-

(a) (ii)

(b) (iii)

(c) (iv)

(d) (i)

 

Exercise 15.2

(1) Use isometric dot paper and make an isometric sketch for each one of the given shapes:

Diagram of Question 1 of Exercise 15.2 of NCERT Chapter Visualising Solid Shapes                       

               (i)                                                                                     (ii)

 

 

                              

 (iii)                                                                                             (iv)

 

Ans-Isometric sketches of given figures are shown below:

(i)

 

 

(ii)

 

(iii)

 

(iv)

 

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

Ans- Three different isometric sketches of a cuboid with dimensions 5 cm, 3 cm, 2 cm are given below:

(i)

 

 

Diagram of Question 2 of Exercise 15.2 of NCERT Chapter Visualising Solid Shapes

 

(ii)

 

(iii)

 

(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.

Ans-

The oblique sketch of cube with 2 cm edge is given below:

 

Diagram of Question 3 of Exercise 15.2 of NCERT Chapter Visualising Solid Shapes

 

The isometric sketch of cube with 2 cm edge is given below:

 

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

(i)

Diagram of Question 4 of Exercise 15.2 of NCERT Chapter Visualising Solid Shapes

 

(ii)

 

 

Ans-

The oblique sketches of given isometric shapes are given below:

 

(i)

 

 

 

(ii)

 

 

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

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

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

Ans-

(a) A cuboid of dimensions 5 cm, 3 cm, 2 cm.

 

(i) An oblique sketch

(ii) An Isometric sketch

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

(i) An oblique sketch

(ii) An isometric sketch

 

(6) An isometric sheet is attached at the end of the book. You could try to make on it some cubes or cuboids of dimensions specified by your friend.

Ans-

Isometric sketches of the cubes and cuboids are given below:

 

Diagram of Question 6 of Exercise 15.2 of NCERT Chapter Visualising Solid Shapes

 

Exercise 15.3

(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

Ans-

Required cross – sections of given solids are shown below:

(a) A brick

(i) Vertical cut

Diagram of Vertical Cut Cross- Section of a Brick

We will get a rectangle after vertical cut of a brick.

(ii) Horizontal cut

Diagram of Horizontal Cut Cross- Section of a Brick

We will get a rectangle after horizontal cut of a brick.

 

(b) A round apple

(i) Vertical cut

 

Diagram of Vertical Cut Cross- Section of a Round Apple

We will get a circle after vertical cut of a round apple.

 

(ii) Horizontal cut

Diagram of Horizontal Cut Cross- Section of a Round Apple

We will get a circle after horizontal cut of a round apple.

 

(c) A die

(i) Vertical Cut

 

Diagram of Vertical Cut Cross- Section of a Die

We will get a square after vertical cut of a die.

 

(ii) Horizontal cut

Diagram of Horizontal Cut Cross- Section of a Die

We will get a square after horizontal cut of a die.

 

(d) A circular pipe

(i) Vertical cut

 

Diagram of Vertical Cut Cross- Section of a Circular Pipe

We will get a rectangle after vertical cut of a circular pipe.

 

(ii) Horizontal cut

Diagram of Horizontal Cut Cross- Section of a Circular Pipe

We will get a circle after horizontal cut of a circular pipe.

 

(e) An ice cream cone

(i) Vertical cut

 

Diagram of Vertical Cut Cross- Section of an Ice Cream Cone

We will get a triangle after vertical cut of an ice cream cone.

 

(ii) Horizontal cut

Diagram of Horizontal Cut Cross- Section of an Ice Cream Cone

We will get a hollow circle after horizontal cut of an ice cream cone.

 

Exercise 15.4

(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.

 

Diagram of Question 1 of Exercise 15.3 of NCERT Chapter Visualising Solid Shapes                                                       

A ball                                             A cylindrical pipe                            A book

(i)                                                               (ii)                                            (iii)

 

Ans-Shadows of given objects are given below:

(i) A ball

 

Shadow shape is circle.

 

(ii) A cylindrical pipe

 

 

Shadow shape is rectangle.

 

(iii) A book

 

Shadow shape is rectangle.

 

(2) Here are the shadows of some 3-D objects, when seen under the lamp of an overrated projector. Identify the solid(s) that match each shadow. (There may be multiple answers for these!)

 

 

               A circle                                                                A square     

Visualising solid shapes,Q 2,Ex - 15.4,diagram(i),NCERT                                  Visualising solid shapes,Q 2,Ex - 15.4,diagram(ii),NCERT

  (i)                                                                           (ii)

 

 

              A triangle                                                                         A rectangle

Visualising solid shapes,Q 2,Ex - 15.4,diagram(iii),NCERT                            Visualising solid shapes,Q 2,Ex - 15.4,diagram(iv),NCERT

 (iii)                                                                                   (iv)

Ans-

Name of the solids that match to the given shadows :

(i) Round plate

(ii) Dice

(iii) Clown cap

(iv) Key board

 

(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.

Ans-

(i) The cube can not cast shadow in the shape of a rectangle. It can cast shadow only in the shape of square.

(ii) The cube can not cast shadow in the shape of a hexagon. It can cast shadow only in the shape of square.

 

Helping Topics

Visualising Solid Shapes  

 

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