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Buddha wants to make a paper cube using a squared sheet. He knows that all the faces of a cube are squares.

He draws two different shapes.

• Will both these shapes fold into a cube?

• Draw at least one more shape which can fold into a cube.

• What will be the area of each face of the cube?

• Draw one shape which will not fold into a cube.

• Look around and discuss which things around you look like a cube. List a few.

**Solution:**

• Yes, both the shapes will fold into a cube.

• The shape which can fold into a cube is shown below.

• We know that, each face of the cube is a small square. Area of small square is 1 square cm. Thus, the area of each face of the cube is 1 square cm.

• The shape which cannot fold into a cube is shown below.

• The shape of die, sugar cubes, ice cubes, etc. resembles that of a cube.

All boxes are not cubes. Here are some different kinds of boxes. Match each shape below with a box into which it will fold.

**Solution:**

For making a house a floor map is first made. Have you ever seen a floor map? Here is a floor map of Vibha's house. It shows where the windows and the doors are in the house.

• Which is the front side of her house? How many windows are there on the front side?

(a)

(b)

(c)

(d)

Here are four **deep drawings** of houses.

• Which one is Vibha's house?

• Why do the other three deep drawings not match the floor map? Discuss.

**Solution:**

• Front side of Vibha's house is encircled in the above image.There are two windows and one door on the front side of the house.

• The front side of Vibha's house has one door and two windows.

• The figure (c) represents Vibha's house.

Look at this floor map of a house. Make doors and windows on the deep drawing of this house.

• Are there any windows you couldn't show on the deep drawing? Circle them on the floor map.

**Solution:**

The doors and windows on the deep drawing of the house is shown below.

There are 2 windows that could not be shown on the deep drawing. These windows are encircled on the floor map as shown below.

Soumitro and his friends made deep drawings of a cube.

These are their drawings.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

• Which of the drawings look correct to you? Discuss.

• Can you add some lines to make drawing (f) into a deep drawing of the cube?

**Solution:**

• The drawings (d), (e) and (g) are correct.

• The deep drawing of a cube after adding lines to figure (f) is shown below:

This cut-out is folded to make a cube.

Which of these are the correct deep drawings of that cube?

(a)

(b)

(c)

(d)

(e)

**Solution:**

The correct deep drawings of the given cube are :

Make a deep drawing of a box which looks like this.

**Solution:**

The deep drawing of the given box is shown below.

• If you look at the bridge from the top, how will it look? Choose the right drawing below:

a)

b)

• Look at the photo and try to make a deep drawing of this bridge.

**Solution:**

The top view of the bridge is shown below.

The deep drawing of the bridge is shown below.

Make drawings to show how this bridge will look

• From the top

• From the front

• From the side

**Solution:**

The top view of the bridge is shown below.

The front view of the bridge is shown below.

The side view of the bridge is shown below.

Make a matchbox model which looks like this.

• Also make a deep drawing of the model in your notebook.

**Solution:**

**Disclaimer: **Students are advised to prepare the answer on their own.

How many cubes are needed to make this interesting model?

• Here are some drawings of the model. Mark the correct top view drawing with 'T' and the correct side view drawing with 'S'.

(a)

(b)

(c)

(d)

**Solution:**

Number of cubes in the top layer = 4 + 5 = 9

Number of cubes in the second layer from top = 4 + 5 + 3 + 4 = 16

Number of cubes in the third layer from top = 4 + 5 + 3 + 4 + 2 + 3 = 21

Number of cubes in the fourth layer from top = 4 + 5 + 3 + 4 + 2 + 3 + 2 + 1 = 24

Number of cubes in the bottom layer = 4 + 5 + 3 + 4 + 2 + 3 + 2 + 1 + 1 = 25

Total number of cubes in the model = 9 + 16 + 21 + 24 + 25 = 95

The correct drawing for the top and side view is given below:

T , S