Exploring Visualising Solid Shapes Chapter 15 of NCERT Class 7 Maths, titled "Visualising Solid Shapes," offers students a profound understanding of three-dimensional geometrical figures. The chapter consists of four exercises, each packed with a variety of questions to challenge and enhance students' comprehension. This collection of NCERT Solutions for Class 7 Maths furnishes comprehensive answers to all exercises, equipping students with a valuable resource for exam preparation.

Download PDF

Question 1 :

**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.)**

Answer :

In the given net there are 3 faces and it can be completed as shown below,

Question 2 :

** Match the nets with appropriate solids:**

Answer :

(a) (ii)

Because, the net (ii) can be folded as a square.

(b) (iii)

Because, the net (iii) can be folded as a cylinder.

(c) (iv)

Because, the net (iv) can be folded as cone.

(d) (i)

Because, the net (i) can be folded as a pyramid.

Question 3 :

**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 :

(i) The given net cannot be folded as a cube.

Because, it can be folded as below,

(ii) The given net can be folded as a cube.

Because, it can be folded as below,

(iii) The given net can be folded as a cube.

Because, it can be folded as below,

(iv) The given net can be folded as a cube.

Because, it can be folded as below,

(v) The given net cannot be folded as a cube.

Because, it can be folded as below,

(vi) The given net can be folded as a cube.

Because, it can be folded as below,

Question 4 :

**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)

By observing the above figure the sum of the opposite faces is equal to 7.

So, the given net can be folded into a net of dice.

(ii)

By observing the above figure the sum of the opposite faces is equal to 7.

So, the given net can be folded into a net of dice.

Question 5 :

**Can this be a net for a die?**

**Explain your answer.**

Answer :

The given net is folded as dice is shown in the figure below,

No, this cannot be a net for a die.

By observing the figure we can say that, one pair of opposite face will have 1 and 4, another pair of opposite face will have 3 and 6 the sum of these two opposite faces are not equal to 7.

Question 1 :

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

**(i)**

**(ii)**

Answer :

(i)

(ii)

Question 2 :

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

Answer :

It is given that the dimensions of a cuboid are 5 cm, 3 cm, and 2 cm.

The three different isometric sketches of this cuboid are shown below:

(i)

(ii)

(iii)

Question 3 :

**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)

Question 4 :

**Three cubes, each with a 2 cm edge, are placed side by side to form a cuboid. Sketch an oblique and isometric sketch of this cuboid.**

Answer :

Oblique sketch

Isometric sketch

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) (i) Oblique sketch

(ii) Isometric sketch

(b) (i) Oblique sketch

(ii) Isometric sketch

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 :

The cross-section of a brick when it is cut into vertically is as shown in the figure below,

The cross-section of a brick when it is cut into horizontally is as shown in the figure below,

(b)

The cross-section of a round apple when it is cut into vertically is as shown in the figure below,

The cross-section of a round apple when it is cut into horizontally is as shown in the figure below,

(c)

The cross-section of a die when it is cut into vertically is as shown in the figure below,

The cross-section of a die when it is cut into horizontally is as shown in the figure below,

(d)

The cross-section of a circular pipe when it is cut into vertically is as shown in the figure below,

The cross-section of a circular pipe when it is cut into horizontally is as shown in the figure below,

(e)

The cross-section of an ice cream when it is cut into vertically is as shown in the figure below,

The cross-section of an ice cream when it is cut into horizontally is as shown in the figure below,

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).**

**(i)**

**(ii)**

**(iii)**

Answer :

(i)

The shape of the shadow obtained from the ball is a circle.

(ii)

The shape of the shadow obtained from the cylindrical pipe is a rectangle.

(iii)

The shape of the shadow obtained from the book is a rectangle.

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)**

Answer :

(i) Cricket ball, water bottle cap, Disc

(ii) Die, chalk box etc.

(iii) Birthday cap, pizza slice etc.

(iv) Book, keyboard, mobile etc.

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) The above statement is true.

(ii) The above statement is false.

Admissions open for 2024-2025

Copyright @2024 | K12 Techno Services ®

ORCHIDS - The International School | Terms | Privacy Policy | Cancellation