Chapter -15 Visualising Solid Shapes | Class 7th |NCERT Maths Solutions | Edugrown

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

(ii)

(iii)

(iv)

(v)

(vi)

Solution:
Cube’s nets are (ii), (iii), (iv) and (vi).

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.
(i)

(ii)

Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total 7.
Solution:
According to the given condition, that opposite faces of a die always have a total of 7 dots on them, we insert the suitable numbers in the blanks as follows:
(i)

(ii)

Question 3.
Can this be a net for a die? Explain your answer.

Solution:
No; Because one pair of opposite faces will have 1 and 4 on them whose total is not 7 and another pair of opposite faces will have 3 and 6 on them whose total is also not 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 are there on the net here? (Give two-separate diagrams. If you like, you may use a squared sheet for easy manipulation.)

Solution:
A cube has six faces, so the complete net for making a cube in at least two different ways are as follows :
(i)

(ii)

Question 5.
Match the nets with appropriate solids:

Solution:
After matching the nets with appropriate solids, we get the following pairs:
(a) – (ii)
(b) – (iii)
(c) – (iv)
(d) – (i)

Question 1.
Use isometric dot paper and make an isometric sketch to teach one of the given shapes :
(i)

Solution:

(ii)

Solution:

(iii)

Solution:

(iv)

Solution:

Question 2.
The dimensions of a cuboid are 5 cm, 3 cm, and 2 cm. Draw three different isometric sketches of this cuboid.
Solution:
Given, the dimensions of a cuboid are 5 cm, 3 cm, and 2 cm. Three different isometric sketches of a cuboid are as follows :

(i) When the length and height of the front face are 5 cm and 3 cm, respectively.

(ii) When the length and height of the front face are 2 cm and 5 cm, respectively.

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

Question 3.
There cubes each with a 2 cm edge are placed side by side to form a cuboid. Sketch an oblique or isometric sketch of this cuboid.
Solution:
Oblique sketch:

Isometric sketch:

Question 4.
Make an oblique sketch for each one of the given isometric shapes.
(i)

Solution:
We know that an oblique sketch does not have proportional lengths but it conveys all important aspects of the appearance of the solid. So, oblique sketch for each one of the appearances of the solid. So, the oblique sketch for each one of the given isometric sketch is as follows:

(ii)

Solution:
We know that an oblique sketch does not have proportional lengths but it conveys all important aspects of the appearance of the solid. So, oblique sketch for each one of the appearances of the solid. So, the oblique sketch for each one of the given isometric sketch is 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?
Solution:
(a)
(i) Oblique sketch of a cuboid of dimensions 5 cm, 3 cm, and 2 cm is as follows:

(ii) An isometric sketch of this cuboid is as follows :

No, these sketches are not unique.

(b) A cube with an edge 4 cm long.
Solution:
(i) Oblique sketch of the cube of edge 4 cm is as follows :

(ii) An isometric sketch of this cube is as follows:

Question 1.
A bulb is kept burnings 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).
(i)

(ii)

(iii)

Solution:

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

(ii)

(iii)

(iv)

Solution:

Question 3.
Examine if the following are true statements :

(i) The cube can cast a shadow in the shape of a rectangle.
Solution:
True, 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.
Solution:
False, the cube can not cast a shadow in the shape of a hexagon.