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This pdf includes the following topics:-

Surface Area of a Cube

The lateral surface area of a cube

Examples with step-by-step explanation.

Surface Area of a Cube

The lateral surface area of a cube

Examples with step-by-step explanation.

1.
Surface Area of a Cube

Cube: In our everyday life, we come across objects like a dice,

Rubik’s cube, Sugar cube, and Ice cube, etc. These objects are in the

shape of a cube. All these objects are made of six square plane

Dice Rubik's cube

Sugar cubes Ice cube

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Cube: In our everyday life, we come across objects like a dice,

Rubik’s cube, Sugar cube, and Ice cube, etc. These objects are in the

shape of a cube. All these objects are made of six square plane

Dice Rubik's cube

Sugar cubes Ice cube

www.edusaksham.com 1

2.
A cube is a three-dimensional shape whose length, breadth and

height are all equal. The cube has six surfaces called faces. Each

face of a cube is a square, two adjacent faces of a cube meet in a

line segment called edge and all of a cube's corners (called vertices)

are right angles. Ultimately, a cube has the shape of a square box.

A B

C

G

B

F H

E D

A cube has six faces (FHDE, FAGE, ABCG BCHD, ABFH & GCDE), eight

vertices (A, B, C, D, E, F, G & H), twelve edges (AB, BC, CG, GA, BH,

HD, DC, DE, FE, FH, AF, & GE).

In the case of a cube, its length, breadth, and height are equal.

Then, side of cube = Length = Breadth = Height

So, the figure with these dimensions would be like the shape

shown below. Here, side of cube = a.

a

a 5 a

a a a a

a 1 a 2 a 3 a 4 a

a a a a

a 6 a

a

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a

height are all equal. The cube has six surfaces called faces. Each

face of a cube is a square, two adjacent faces of a cube meet in a

line segment called edge and all of a cube's corners (called vertices)

are right angles. Ultimately, a cube has the shape of a square box.

A B

C

G

B

F H

E D

A cube has six faces (FHDE, FAGE, ABCG BCHD, ABFH & GCDE), eight

vertices (A, B, C, D, E, F, G & H), twelve edges (AB, BC, CG, GA, BH,

HD, DC, DE, FE, FH, AF, & GE).

In the case of a cube, its length, breadth, and height are equal.

Then, side of cube = Length = Breadth = Height

So, the figure with these dimensions would be like the shape

shown below. Here, side of cube = a.

a

a 5 a

a a a a

a 1 a 2 a 3 a 4 a

a a a a

a 6 a

a

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a

3.
So, the sum of the areas of the six squares is:

Area of square 1 = (𝐚 × 𝐚) + Area of square 2 = (𝐚 × 𝐚) + Area of

square 3 = (𝐚 × 𝐚) + Area of square 4 = (𝐚 × 𝐚) + Area of square 5

= (𝐚 × 𝐚) + Area of square 6 = (𝐚 × 𝐚).

⇒Surface Area of Cube = 𝟐(𝐚 × 𝐚) + 𝟐(𝐚 × 𝐚) + 𝟐(𝐚 × 𝐚).

= 𝟐[(𝐚 × 𝐚) + (𝐚 × 𝐚) + (𝐚 × 𝐚)].

= 𝟐(𝐚𝟐 + 𝐚𝟐 + 𝐚𝟐 ).

= 𝟐(𝟑𝐚𝟐 ).

= 6 𝐚𝟐 .

Where a is the length of edges of the cube.

Surface Area of Cube = 6 𝐚𝟐

Example: Find the surface area of a Rubik’s cube whose edge is 6

6 cm 6 cm

6 cm

Solution: Clearly, Rubik’s cube is in the form of a cube.

Here, edge of Rubik’s cube = a = 6 cm.

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Area of square 1 = (𝐚 × 𝐚) + Area of square 2 = (𝐚 × 𝐚) + Area of

square 3 = (𝐚 × 𝐚) + Area of square 4 = (𝐚 × 𝐚) + Area of square 5

= (𝐚 × 𝐚) + Area of square 6 = (𝐚 × 𝐚).

⇒Surface Area of Cube = 𝟐(𝐚 × 𝐚) + 𝟐(𝐚 × 𝐚) + 𝟐(𝐚 × 𝐚).

= 𝟐[(𝐚 × 𝐚) + (𝐚 × 𝐚) + (𝐚 × 𝐚)].

= 𝟐(𝐚𝟐 + 𝐚𝟐 + 𝐚𝟐 ).

= 𝟐(𝟑𝐚𝟐 ).

= 6 𝐚𝟐 .

Where a is the length of edges of the cube.

Surface Area of Cube = 6 𝐚𝟐

Example: Find the surface area of a Rubik’s cube whose edge is 6

6 cm 6 cm

6 cm

Solution: Clearly, Rubik’s cube is in the form of a cube.

Here, edge of Rubik’s cube = a = 6 cm.

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4.
Therefore, the surface area of Rubik’s cube = 6𝐚𝟐 .

= 6(𝟔𝟐 )𝐜𝐦𝟐 .

= 6 × 36 𝐜𝐦𝟐 .

= 216 𝐜𝐦𝟐 .

Hence, the surface area of Rubik's cube = 216 𝐜𝐦𝟐 .

Lateral Surface Area of a Cube: If out of the six faces of a cube, we

only find the sum of the areas of four faces leaving the bottom and

top faces. This sum is called the lateral surface area of the cube.

Consider a cube of the side as ‘a’ which is shown in the figure

below. A B

C

G

B

a

H

F

a

E a D

Lateral surface area of cube

= Area of face HBCD + Area of face CDEG + Area of face GEFA + Area

of face ABHF.

= (𝐚 × 𝐚) + (𝐚 × 𝐚) + (𝐚 × 𝐚) + (𝐚 × 𝐚).

= 𝐚𝟐 + 𝐚𝟐 + 𝐚𝟐 +𝐚𝟐 = 𝟒𝐚𝟐 .

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= 6(𝟔𝟐 )𝐜𝐦𝟐 .

= 6 × 36 𝐜𝐦𝟐 .

= 216 𝐜𝐦𝟐 .

Hence, the surface area of Rubik's cube = 216 𝐜𝐦𝟐 .

Lateral Surface Area of a Cube: If out of the six faces of a cube, we

only find the sum of the areas of four faces leaving the bottom and

top faces. This sum is called the lateral surface area of the cube.

Consider a cube of the side as ‘a’ which is shown in the figure

below. A B

C

G

B

a

H

F

a

E a D

Lateral surface area of cube

= Area of face HBCD + Area of face CDEG + Area of face GEFA + Area

of face ABHF.

= (𝐚 × 𝐚) + (𝐚 × 𝐚) + (𝐚 × 𝐚) + (𝐚 × 𝐚).

= 𝐚𝟐 + 𝐚𝟐 + 𝐚𝟐 +𝐚𝟐 = 𝟒𝐚𝟐 .

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5.
Lateral surface area of a cube = 4𝐚𝟐

Example 1: Find the lateral surface area of a dice whose edge is 5

cm.

5 cm

Solution: Clearly, dice is in the form of a cube.

Here, length of edge of dice = a = 5 cm.

Therefore, Lateral surface area of the dice = 4𝐚𝟐 .

= 4(𝟓𝟐 )𝐜𝐦𝟐 .

= 4 × 25 𝐜𝐦𝟐 .

= 100 𝐜𝐦𝟐 .

Hence, the lateral surface area of the dice = 100 𝐜𝐦𝟐 .

Example 2:Five cubes each of side 5 cm are joined end to end. Find

the surface area of the resulting cuboid.

5

cm

5 cm

5 cm 5 cm 5 cm 5 cm 5 cm

Solution: The dimensions of the cuboid so formed are as under :

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Example 1: Find the lateral surface area of a dice whose edge is 5

cm.

5 cm

Solution: Clearly, dice is in the form of a cube.

Here, length of edge of dice = a = 5 cm.

Therefore, Lateral surface area of the dice = 4𝐚𝟐 .

= 4(𝟓𝟐 )𝐜𝐦𝟐 .

= 4 × 25 𝐜𝐦𝟐 .

= 100 𝐜𝐦𝟐 .

Hence, the lateral surface area of the dice = 100 𝐜𝐦𝟐 .

Example 2:Five cubes each of side 5 cm are joined end to end. Find

the surface area of the resulting cuboid.

5

cm

5 cm

5 cm 5 cm 5 cm 5 cm 5 cm

Solution: The dimensions of the cuboid so formed are as under :

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6.
𝒍 = length = (5+5+5+5+5) cm = 25 cm,

𝒃 = breadth = 5 cm and 𝒉 = height = 5 cm.

So, surface area of the cuboid = 𝟐(𝒍𝒃 + 𝒃𝒉 + 𝒍𝒉).

= 2(𝟐𝟓 𝐜𝐦 × 𝟓 𝐜𝐦 + 𝟓 𝐜𝐦 × 𝟓 𝐜𝐦 + 𝟐𝟓 𝐜𝐦 × 𝟓 𝐜𝐦).

= 2(𝟏𝟐𝟓 𝐜𝐦𝟐 + 𝟐𝟓 𝐜𝐦𝟐 + 𝟏𝟐𝟓 𝐜𝐦𝟐 ).

= 2(𝟐𝟕𝟓 𝐜𝐦𝟐 ).

= 𝟓𝟓𝟎 𝐜𝐦𝟐 .

Hence, Surface area of the cuboid formed = 550 𝐜𝐦𝟐 .

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𝒃 = breadth = 5 cm and 𝒉 = height = 5 cm.

So, surface area of the cuboid = 𝟐(𝒍𝒃 + 𝒃𝒉 + 𝒍𝒉).

= 2(𝟐𝟓 𝐜𝐦 × 𝟓 𝐜𝐦 + 𝟓 𝐜𝐦 × 𝟓 𝐜𝐦 + 𝟐𝟓 𝐜𝐦 × 𝟓 𝐜𝐦).

= 2(𝟏𝟐𝟓 𝐜𝐦𝟐 + 𝟐𝟓 𝐜𝐦𝟐 + 𝟏𝟐𝟓 𝐜𝐦𝟐 ).

= 2(𝟐𝟕𝟓 𝐜𝐦𝟐 ).

= 𝟓𝟓𝟎 𝐜𝐦𝟐 .

Hence, Surface area of the cuboid formed = 550 𝐜𝐦𝟐 .

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