# Surface Area of Cube

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Cube means the area required for making the cube. After unfolding it we get the area of each face. The total area of each face which is in square shape gives us the Surface area of cubical shape.

From the above figure, we can see that there are 6 faces and each face is of square shape.

Surface area = 6 x (side )^{2} = 6a^{2}Lateral surface area = 4a ^{2}Diagonal of Cube = (√3) a |

**Some solved examples on surface area of cube**

1) Find the ratio of the total surface area and lateral surface area of a cube.

**Solution :**

Total surface area of cube = 6 a

^{2}

Lateral surface area = 4 a

^{2}

∴ TSA / LSA = 6 a

^{2}/ 4 a

^{2}

⇒ = 3 / 2

∴ The ratio is 3 : 2.

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2) A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes.

**Solution**

TSA of big cube = 6 a

^{2}= 6 x 4

^{2}= 96 cm

^{2}

TSA of small cube = 6 x 1 x 1 = 6 cm

^{2}

Number of new cubes 4 / 1 = 4

∴ TSA of all small cubes = 96 x 4 = 384 cm

^{2}

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3) Each edge of a cube is increase by 50%. Find the percentage increase in the surface are of the cube.

**Solution :**

Let the edge = a cm

So increase by 50 % = a + a/ 2 = 3a / 2

TSA of original cube = 6 a

^{2}

TSA of new cube = 6 ( 3a/ 2)

^{2}

= 6 x 9a

^{2}/ 4 = 54a

^{2}/ 4 = 13.5a

^{2}

Increase in area = 13.5a

^{2}- 6 a

^{2}

= 7.5a

^{2}Increase % = ( 7.5a

^{2}/ 6 a

^{2}) x 100 = 125%

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4) Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new rectangular prism ( cuboid ) to that of the sum of the surface areas of the three cubes.

**Solution :**

TSA of cube = 6a

^{2}

Length of new rectangular prism = 3a , width = a and height = a

TSA of rectangular prism = 2( lw + wh + lh)

⇒ = 2 (3a x a + a x a + 3a x a)

⇒ = 2 ( 3a

^{2}+ a

^{2}+ 3a

^{2})

⇒ = 2 ( 7a

^{2})

TSA of rectangular prism = 14a

^{2}

∴ TSA of rectangular prism / TSA of a cube 3 cubes = (14a

^{2}) / 18a

^{2}

∴ Ratio = 14 / 18 = 7 / 9

∴ The ratio is 7 : 9

**Surface Area :**

• Surface Area of Cube

• Surface Area of Rectangular Prism(Cuboid)

• Surface Area of Cylinder

• Surface Area of Cone

• Surface Area of Sphere and Hemisphere

• Surface Area of Prism

• Surface Area of Pyramid

• Surface Area of Cube

• Surface Area of Rectangular Prism(Cuboid)

• Surface Area of Cylinder

• Surface Area of Cone

• Surface Area of Sphere and Hemisphere

• Surface Area of Prism

• Surface Area of Pyramid

8th grade math

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