# Surface Area of Cube

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In this section we will discuss Surface Area of Cube :

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 = 6a2 Lateral surface area = 4a2 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 a2
Lateral surface area = 4 a2
∴ TSA / LSA = 6 a2 / 4 a2
⇒ = 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 a2 = 6 x 42 = 96 cm2
TSA of small cube = 6 x 1 x 1 = 6 cm2
Number of new cubes 4 / 1 = 4
∴ TSA of all small cubes = 96 x 4 = 384 cm2
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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 a2
TSA of new cube = 6 ( 3a/ 2)2
= 6 x 9a2/ 4 = 54a2 / 4 = 13.5a2
Increase in area = 13.5a2 - 6 a2
= 7.5a2 Increase % = ( 7.5a2 / 6 a2) 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 = 6a2
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 ( 3a2 + a2 + 3a2)
⇒ = 2 ( 7a2)
TSA of rectangular prism = 14a2
∴ TSA of rectangular prism / TSA of a cube 3 cubes = (14a2) / 18a2
∴ 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

From cube to Mensuration