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Similarly, the lateral surface area of a cube can be calculated using lateral
surface area of a cuboid = 2h(l + b)

Let us replace each dimension with ‘a’. a
a
So, lateral surface area of a cube = 2a(a + a) = 2a(2a) = 4a 2

2
Thus, the lateral surface area of a cube = 4a sq. units.
Example 18: Find the total surface area and lateral surface area of a cube having a side of 8 cm.

Solution: Here, side of the cube, a = 8 cm.
2
2
We have, the total surface area of a cube = 6a = 6(8 cm) = 384 cm 2
2
2
And, the lateral surface area of the cube = 4a = 4(8 cm) = 256 cm 2
2
2
Thus, the total surface area of the given cube is 384 cm and the lateral surface area is 256 cm .
2
Example 19: Find the side of a cube whose surface area is 216 cm .
Solution: Let the side of the given cube be a cm.
Think and Answer
We have, total surface area of cube = 6a 2
Three cubes each with side
\ 6a = 216 cm 2 (Given) 3 cm are joined to form a cuboid.
2

2
2
⇒ a = 216 cm = 36 cm 2 What is the surface area of this
cuboid?
6
⇒ a = 36 cm = 6 cm 3 cm
3 cm 3 cm 3 cm
Thus, the side of the given cube is 6 cm. 3 cm
Example 20: A cubical carton with a side measure of 80 cm is to be covered with a plastic sheet.
How long a sheet of width 96 cm is required to cover 30 such cartons?

Solution: Here, side of the cubical carton, a = 80 cm
2
Total surface area of the cubical carton = 6a = 6 × (80 cm) = 6 × 6400 cm = 38400 cm 2
2
2
2
\ Surface area of 30 such cubical cartons = 38400 cm × 30 = 1152000 cm 2
So, the area of plastic sheet needed to cover these 30 cartons = 1152000 cm 2
Now, width of plastic sheet = 96 cm (Given)
Area of plastic sheet needed 1152000
\ Required length of plastic sheet = = cm
Width of sheet 96
12000
= 12000 cm = m [Q 1 m = 100 cm]
100
= 120 m.
Cylinder

Another common three-dimensional shape with two identical faces Flat face
is the cylinder. Soft drink cans, tubelights, battery cells, etc., are Edge
common cylindrical objects we see around us. h Curved face
A cylinder consists of two identical flat faces and one curved face Flat face
as shown. r

245 Mensuration