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Example 15: What will be the lateral surface area of a cuboid whose dimensions are
12 cm × 10 cm × 6 cm?
Solution: Here, length = 12 cm, breadth = 10 cm, and height = 6 cm

2
2
\ Lateral surface area of the cuboid = 2h(l + b) = 2 × 6 × (12 + 10) cm = 12(22) cm = 264 cm .
Example 16: Nisha wants to cover the four sides of a box of dimensions 4 m × 3 m × 1.5 m with
a glazed paper sheet. How much glazed paper will be required if we assume that the paper fits
exactly the outer surface of the box?
Solution: Let l = 4 m, b = 3 m, and h = 1.5 m be the dimensions of the cuboidal box.

Area of 4 walls (sides of box) = Lateral surface area
= 2(l + b)h = 2(4 + 3) m × 1.5 m = 2 × 7 m × 1.5 m
= 14 m × 1.5 m = 21 m 2

2
Thus, Nisha needs 21 m glazed paper to cover the 4 sides of the box.
Example 17: The dimensions of a cuboid are in the ratio 2 : 3 : 5 and its total surface area is
248 cm . Find the dimensions of the cuboid.
2
Solution: Since, the dimensions of the cuboid are in the ratio 2 : 3 : 5.

Let the dimensions be l = 2x, b = 3x, and h = 5x.
2
Also, it is given that the total surface area of cuboid = 248 cm .
Q Total Surface area of the cuboid = 2(lb + bh + hl)
2
2
2
2
\ 2(2x × 3x + 3x × 5x + 5x × 2x) = 248 cm ⇒ 2(6x + 15x + 10x ) = 248 cm 2
2
2
2
⇒ 2 × 31x = 248 cm ⇒ 62x = 248 cm 2
248
2
⇒ x = cm = 4 cm 2
2
62
\ x = 2 cm
Putting, x = 2, the dimensions of the cuboid are l = 2x = 2 × 2 cm = 4 cm, b = 3x = 3 × 2 cm = 6 cm and
h = 5x = 5 × 2 cm = 10 cm
Thus, the length, breadth and height of the cuboid are 4 cm, 6 cm and 10 cm, respectively.
Cube
A cube is a cuboid whose all three dimensions, that is, length, breadth, and height are the same.
Surface Area of a Cube

Since a cube is a special cuboid with all dimensions being equal, we can derive the formulae of
total surface area and lateral surface area of a cube with the help of the formulae of a cuboid.

Total surface area of a cuboid = 2(lb + bh + hl)
Let us replace each dimension by ‘a’.
a
So, total surface area of a cube = 2(a × a + a × a + a × a) a
a a
2
= 2(a + a + a ) a a
2
2
2
= 2(3a ) a
2
= 6a sq. units In general, total surface area can
2
Therefore, the total surface area of a cube = 6a sq. units Note: also be referred as surface area.
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