# Chapter – 15: Visualizing Solid Shapes

## Exercise 15.1

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

**(i)**

**Solution: –**

The given net cannot be folded as cube.

Because, it can be folded as below,

**(ii)**

**Solution: –**

The given net can be folded as cube.

Because, it can be folded as below,

**(iii)**

**Solution: –**

The given net can be folded as cube.

Because, it can be folded as below,

**(iv)**

**Solution: –**

The given net can be folded as cube.

Because, it can be folded as below,

**(v)**

**Solution: –**

The given net cannot be folded as cube.

Because, it can be folded as below,

**(vi)**

**Solution: –**

The given net can be folded as cube.

Because, it can be folded as below,

**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.**

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

**Solution: –**

**(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.

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

**Explain your answer.**

**Solution: –**

The given net is folded as dice is shown in 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.

**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.)**

**Solution: –**

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

**5. Match the nets with appropriate solids:**

**Solution: –**

**(a) (ii)**

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

**(b) (iii)**

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

**(c) (iv)**

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

**(d) (i)**

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

## Exercise 15.2

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

**(i)**

Solution: –

**(ii)**

**Solution: –**

**(iii)**

**Solution: –**

**(iv)**

**Solution: –**

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

**Solution: –**

From the question it is given that dimension of a cuboid are 5 cm, 3 cm, and 2 cm.

The three different isometric sketches of this cuboid is shown below,

1

2

**3**

**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.**

**Solution: –**

Oblique sketch

Isometric sketch

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

**(i)**

**Solution: –**

**(ii)**

**Solution: –**

**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.**

**Solution: –**

(a)

**(i) **Oblique sketch

**(ii)** Isometric sketch

(b)

**(i) **Oblique sketch

**(ii)** Isometric sketch

## 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**

**Solution: –**

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) A round apple**

**Solution: –**

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) A die**

**Solution: –**

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) A circular pipe**

**Solution: –**

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) An ice cream cone**

**Solution: –**

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,

## 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. (You may try to experiment first and then answer these questions).**

**(i)**

**Solution: –**

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

**(ii)**

**Solution: –**

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

**(iii)**

**Solution: –**

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

**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)**

**Solution: –**

Cricket ball, water bottle cap, Disc

**(ii)**

**Solution: –**

Die, chalk box etc.

**(iii)**

**Solution: –**

Birthday cap etc.

**(iv)**

**Solution: –**

Book, keyboard, Mobile etc.

**3. Examine if the following are true statements:**

**(i) The cube can cast a shadow in the shape of a rectangle.**

**Solution: –**

The above statement is true.

**(ii) The cube can cast a shadow in the shape of a hexagon.**

**Solution: –**

The above statement is false.

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