**NCERT Class 9 Maths Lab Manual – Form a Cube and Find the Formula for its Surface**

**OBJECTIVE**

To form a cube and find the formula for its surface area experimentally.

**Materials Required**

- Cardboard
- Ruler
- Cutter/Scissors
- Adhesive tape
- Pen/Pencil

**Prerequisite Knowledge**

- Knowledge about basic properties of a cube.
- Surface area, lateral surface area and diagonal of a cube.

**Theory**

- For basic properties of a cube refer to Activity 7.
- Surface Area of a Cube

Let each edge of the cube be a units. Then,- Total Surface Area (TSA) of the cube = Sum of areas of six faces

= 6 (area of each faces)

= 6 (a x a)

=> TSA = 6a² sq units - Lateral surface area of the cube

= Sum of areas of four faces only leaving the top and bottom faces = 4(area of each face) = 4 (a x a)

=> Lateral surface area = 4a² sq units - Diagonal of the cube = \(\sqrt { { a }^{ 2 }+{ a }^{ 2 }+{ a }^{ 2 } }\) = \(\sqrt { { 3a }^{ 2 } }\)

=> Diagonal of the cube = √3a units

- Total Surface Area (TSA) of the cube = Sum of areas of six faces

**Procedure**

- Take a cardboard of a suitable size, using cardboard make six identical squares each of side x units.
- Now, arrange all six squares and join all of them with the help of tape, (see Fig. 26.1)

- Fold the square along the dotted markings (or along tape) (see Fig. 26.1) and form a cube using tape, (see Fig. 26.2)

**Demonstration**

Surface area of a cube of side x units =6x (area of each face of cube of side x units)

= 6x² [since, each face of the cube is a square, so area of square = (side)² = (x)² ]

**Note:**

A net of a cube be directly prepared on the cardboard itself instead of making six squares separately.

**Observation**

By actual measurement,

Length of side x = ……….. ,

Area of one square/one face = x² = ……….. ,

So, sum of areas of all the squares = ……….. + ……….. + ……….. + ……….. + ……….. + ………..

Hence, surface area of the cube is 6x².

**Result**

We have verified the formula for calculating the surface area of the cube.

**Application**

This activity may be used in estimation of materials necessary in production of cubical boxes used for packing.

**Viva Voce**

**Question 1:**

How many edges are there in a cube?

**Answer:**

12

**Question 2:**

If each edge of a cube is 3 cm, then what is the area of each face of a cube?

**Answer:**

9 cm².

**Question 3:**

If a room is in the shape of cube of length x units, then what will be the area of room which has to be painted by painter including gate?

**Answer:**

5x² (= 6x² – x²), because one face will be floor of the room.

**Question 4:**

What is the required condition for a room to be in the shape of cube?

**Answer:**

The length, breadth and height of the room should be equal.

**Question 5:**

How will you define a cube?

**Answer:**

A cube is a symmetric three dimensional solid shape bounded by six square faces.

**Question 6:**

Find the maximum length of the rod that can be placed in a cube of side x.

**Answer:**

The maximum length of the rod that can be placed in a cube is equal to the diagonal of the cube, i.e.√3x.

**Question 7:**

How many lateral surfaces a cube have?

**Answer:**

Their are 4 lateral surfaces of a cube.

**Question 8:**

Write three real life examples of cube.

**Answer:**

Dice, sugar free cube, rubiks cube.

**Question 9:**

How many dimensions of a cube?

**Answer:**

A cube has three dimensions.

**Question 10:**

“If we take one surface of a folding paper cube, then it is a two dimensional plane”. Is this statement true?

**Answer:**

Yes

**Suggested Activity**

Using the above activity, find the area of a cube, if each edge of a cube is 6 cm.

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