It is a three dimensional solid having six rectangular faces.
Example: Bricks, Books etc.,
Let l, b and h be the length, breadth and height of a cuboid respectively. To find the
total surface area, we split the faces into three pairs.
(i) The total area of the front and back faces is
lh + lh = 2lh square units.
(ii) The total area of the side faces is
bh + bh = 2bh square units.
(iii) The total area of the top and bottom faces is
lb + lb = 2lb square units.
If the length, breadth and height of a cuboid are l, b and h respectively, then the volume V of the cuboid is given by the formula
V = l ⋅ b ⋅ h cubic units
Example 1 :
Find the total surface area of a cuboid whose length, breadth and height are 20 cm, 12 cm and 9 cm respectively.
Given that l = 20 cm, b = 12 cm, h = 9 cm
T.S.A = 2 (lb + bh + lh)
= 2[(20 ⋅ 12) + (12 ⋅ 9) + (20 ⋅ 9)]
= 2(240 + 108 + 180)
= 2 (528)
= 1056 cm2
Example 2 :
Find the L.S.A of a cuboid whose dimensions are given by 3m ⋅ 5m ⋅ 4m
Given that l = 3 m, b = 5 m, h = 4 m
L.S.A = 2h (l + b)
= 2(4) (3 + 5)
= 8 (8)
= 64 sq. m
Hence the required lateral surface area is 64 sq. m.
Example 3 :
Find the volume of a cuboid whose dimensions are given by 11 m, 10 m and 7 m.
Given that l = 11 m, b = 10 m, h = 7 m
Volume of cuboid = lbh
= 11 ⋅ 10 ⋅ 7
= 770 cu.m.
Example 4 :
Two cubes each of volume 216 cm3 are joined to form a cuboid as shown in the figure.
Find the T.S.A of the resulting cuboid.
Let the side of each cube be a. Then a3 = 216
a = ∛216 = 6 cm
Now the two cubes of side 6 cm are joined to form a cuboid.
l = 6 + 6 = 12 cm, b = 6 cm, h = 6 cm
Total surface area = 2 (lb + bh + lh)
= 2 [(12 ⋅ 6) + (6 ⋅ 6) + (12 ⋅ 6)]
= 2 [72 + 36 + 72]
= 2 ⋅ 180
= 360 cm2
Hence the required total surface area is 360 cm2
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