NCERT Solutions for Class 7 Maths Chapter 15 – Visualizing Solid Shapes
Page No 281:
Question 1:
Identify the nets which can be used to make cubes (cut out copies of the nets and try it):
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1828/Chapter%2015_html_2793bdb.jpg)
Answer:
(i)The given net can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1828/Chapter%2015_html_59186674.jpg)
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.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1828/Chapter%2015_html_47109d38.jpg)
A cube can thus be formed in the above way.
(iii) The given net can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1828/Chapter%2015_html_m5406bdff.jpg)
A cube can thus be formed in the above way.
(iv) The given net can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1828/Chapter%2015_html_1d624172.jpg)
A cube can thus be formed in the above way.
(v) The given net can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1828/Chapter%2015_html_m538ffe83.jpg)
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.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1828/Chapter%2015_html_m69cb43ce.jpg)
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.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1831/Chapter%2015_html_m142efd4.jpg)
Here are two nets to make dice (cubes); the numbers inserted in each square indicate the number of dots in that box.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1831/Chapter%2015_html_m20c91126.jpg)
Insert suitable numbers in the blanks, remembering that the number on the opposite faces should total to 7.
Answer:
(i) The numbers can be inserted as follows so as to make the given net into a net of a dice.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1831/Chapter%2015_html_669ef171.jpg)
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.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1831/Chapter%2015_html_m1a7a6d06.jpg)
It can be observed that the sum of the opposite faces is 7.
Question 3:
Can this be a net for a die?
Explain you answer
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1833/Chapter%2015_html_4c2ef37e.jpg)
Answer:
The given net can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1833/Chapter%2015_html_51fb3b36.jpg)
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.
Page No 282:
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.)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1835/Chapter%2015_html_4a415a2f.jpg)
Answer:
There are 3 faces in the given net. The given net can be completed as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1835/Chapter%2015_html_1e22c41c.jpg)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1835/Chapter%2015_html_m4fb3eec7.jpg)
Question 5:
Match the nets with appropriate solids:
(a)
| ![]() |
(i)
| ![]() |
(b)
| ![]() |
(ii)
| ![]() |
(c)
| ![]() |
(iii)
| ![]() |
(d)
| ![]() |
(iv)
| ![]() |
Answer:
Consider net (i). It can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1842/Chapter%2015_html_67a84691.jpg)
It is a net of a pyramid. Hence, (d) is the correct matching option.
Consider net (ii). It can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1842/Chapter%2015_html_m6e170a28.jpg)
It is a net of a cube. Hence, (a) is the correct matching option.
Consider net (iii). It can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1842/Chapter%2015_html_m2ae779e9.jpg)
It is a net of a cylinder. Hence, (b) is the correct matching option.
Consider net (iv). It can be folded as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1842/Chapter%2015_html_583935a2.jpg)
It is a net of a cone. Hence, (c) is the correct matching option.
Page No 285:
Question 1:
Use isometric dot paper and make an isometric sketch for each one of the given shapes:
![]() | ![]() |
(i)
|
(ii)
|
![]() | ![]() |
(iii)
|
(iv)
|
Answer:
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.
Answer:
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.
Answer:
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:
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1851/Chapter%2015_html_5d7d91e6.jpg)
Answer:
The oblique sketch of these figures will be as follows.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1851/Chapter%2015_html_m4fd7be16.jpg)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1851/Chapter%2015_html_3627e115.jpg)
Page No 286:
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:
(i) Oblique sketch
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1856/Chapter%2015_html_m32972a3d.jpg)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1856/Chapter%2015_html_m51ca4cc5.jpg)
(ii) Isometric sketch
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1856/Chapter%2015_html_m44c58ef1.jpg)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1856/Chapter%2015_html_53097e3f.jpg)
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.
Page No 288:
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:
(a) A brick
We can give a vertical cut to a brick in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_33e9bd86.jpg)
We can give a horizontal cut to a brick in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_m10d8db3b.jpg)
(b) A round apple
We can give a vertical cut to a round apple in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_ff1c967.jpg)
We can give a horizontal cut to a round apple in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_m1bf25d70.jpg)
(c) A die
We can give a vertical cut to a dice in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_6ca7cba0.jpg)
We can give a horizontal cut to a dice in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_1d04261a.jpg)
(d) A circular pipe
We can give a vertical cut to a circular pipe in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_m7e378558.jpg)
We can give a horizontal cut to a circular pipe in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_m21c3b355.jpg)
(e) An ice cream cone
We can give a vertical cut to an ice cream cone in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_m31fb81d8.jpg)
We can give a horizontal cut to an ice cream cone in the following way.
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1866/Chapter%2015_html_m3a7f99cd.jpg)
Page No 289:
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).
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1869/Chapter%2015_html_2665e0f9.jpg)
Answer:
The shapes of the shadows of these figures will be as follows.
(i) A ball
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1869/Chapter%2015_html_5ed3cae2.jpg)
The shape of the shadow of a ball will be a circle.
(ii) A cylindrical pipe
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1869/Chapter%2015_html_m46c5fd0d.jpg)
The shape of the shadow of a circular pipe will be a rectangle.
(iii) A book
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1869/Chapter%2015_html_m75d313af.jpg)
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!)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/7/3/45/1871/Chapter%2015_html_m2c19a8c0.jpg)
Answer:
The given shadows can be obtained in case of the following objects.
- Compact disk
- A dice
- Triangular pyramid
- Note Book
Page No 290:
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:
A cube can cast shadow only in the shape of a square. Therefore, any other shapes are not possible.