Class 7 - Maths - Visualising Solid Shapes

Exercise 15.1

Question 1:

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

   Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets                          

Answer:

(i) The given net can be folded as follows:

           Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets1                                     

When the faces that are in the 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:

           Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets2                                     

A cube can thus be formed in the above way.

(iii) The given net can be folded as follows:

              Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets3                               

A cube can thus be formed in the above way.

(iv) The given net can be folded as follows:

                        Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets4                     

A cube can thus be formed in the above way.

(v) The given net can be folded as follows:

                        Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets5                      

When the faces that are in the 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:

                             Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets6             

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.

                    Class_7_Visualizing_Solid_Shapes_Cube                                        

Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box.

                  Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets7                                      

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

Answer:

(i) The number can be inserted as follows so as to make the given net into a net of a dice.

       Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets8                                              

It can be observed that the sum of the opposite faces is 7

(ii) The number can be inserted as follows so as to make the given net into a net of a dice.

      Class_7_Visualizing_Solid_Shapes_Cubes_Cut_Out_From_Nets9                                            

Question 3:

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

    Class_7_Visualizing_Solid_Shapes_Die_Out_Of_Net                                                    

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.

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

                Class_7_Visualizing_Solid_Shapes_Incomplete_Cube                                    

Answer:

There are 3 faces in the given net. The given net can be completed as follows.

              Class_7_Visualizing_Solid_Shapes_Net1                              Class_7_Visualizing_Solid_Shapes_Net2

Question 5:

Match the nets with appropriate solids:

      Class_7_Visualizing_Solid_Shapes_Different_Shapes1                                                     

Answer:

                                                       

 Class_7_Visualizing_Solid_Shapes_Different_Shapes2

 

                                                                  Exercise 15.2

Question 1:

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

           Class_7_Visualizing_Solid_Shapes_IsometricSketch              

Answer:

(i)

        Class_7_Visualizing_Solid_Shapes_IsometricSketch1                                         

                                       

 

(ii)

 

 Class_7_Visualizing_Solid_Shapes_IsometricSketch2

 

 

 

(iii)

 Class_7_Visualizing_Solid_Shapes_IsometricSketch3

                               

 

(iv)

             Class_7_Visualizing_Solid_Shapes_IsometricSketch4                             

Question 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:

                                            

 Class_7_Visualizing_Solid_Shapes_Cuboid

 

Three different isometric sketches are:

                               Class_7_Visualizing_Solid_Shapes_3_Different_Isometric_Sketches                 

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.

Answer:

Oblique sketch:

               Class_7_Visualizing_Solid_Shapes_Cube_On_Isometric_Sheet                           

Isometric sketch:

         Class_7_Visualizing_Solid_Shapes_Cube_On_Isometric_Sheet1                                 

 

Question 4:

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

                Class_7_Visualizing_Solid_Shapes_Oblique_Sketches                             

Answer:

Oblique sketches:

      Class_7_Visualizing_Solid_Shapes_Oblique_Sketches                                 

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.

Answer:

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

          Class_7_Visualizing_Solid_Shapes_Oblique_&_IsometricSketch1       

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

           Class_7_Visualizing_Solid_Shapes_Oblique_&_IsometricSketch      

Question 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.

Answer:

Cubes and cuboids shapes on isometric sheet given below:

 

        Class_7_Visualizing_Solid_Shapes_3_Cube_&_Cuboid_On_Isometric_Paper          

You can also draw more shapes of cubes and cuboids.

                                                      Exercise 15.3

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.

Answer:

           

 Class_7_Visualizing_Solid_Shapes_3_DifferentShapes

              

                                                              Exercise 15.4

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).

 Class_7_Visualizing_Solid_Shapes_Different_3D_Shapes1

                    

Answer:

          Class_7_Visualizing_Solid_Shapes_Different_Solid_Shapes        

 

 

 

Question 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!)

       Class_7_Visualizing_Solid_Shapes_Different_3D_Shapes            

Answer:

    Class_7_Visualizing_Solid_Shapes_Different_Shapes      

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.

Answer:

(i) True

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

(ii) False

A cube can cast a shadow in the shape of a rectangle.

 

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