Surface Area Of Cuboid
A cuboid is made up of 6 rectangles, and to calculate TSA (Total Surface Area) of Cuboid, you need to sum of the areas of 6 rectangles. Some examples which can be solved through Surface Area of Cuboid Formula have been provided on this web page.
TSA = 2 (lw + wh + hl), l= Length, w= Width and h= Height |
Questions based on LSA (Lateral Surface Area), CSA (Curved Surface Area) and TSA (Total Surface Area) formulas have been asked in many competitive exams. Go through the below section and get the solved examples and complete elaboration of Surface Area of Cuboid Formula.
Surface Area of Cuboid Formula:
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Surface Area Of Cuboid
What is Cuboid?
Cuboid is a closed 3-dimensional geometrical figure made from 6 rectangular plane regions. For example, a matchbox, a tea packet, a chalk box, a dice, a book etc, all these objects have a similar shape. In fact, all these objects are made of six rectangular planes. The shape of these objects is a cuboid.
Faces:
Cuboid is made up of six rectangles and each of the rectangle is called the face. In the figure above, ABFE, DAEH, DCGH, CBFG, ABCD and EFGH are the 6-faces of cuboid. The top face ABCD and bottom face EFGH form a pair of opposite faces. Similarly, ABFE, DCGH, and DAEH, CBFG are pairs of opposite faces.
Any two faces other than the opposite faces are called adjacent faces.
Here, adjacent faces are ABCD, ABFE and ABCD, AEHD.
Know How to Calculate: Surface Area of Cube Formula
Base and Lateral Faces:
Any face of a cuboid may be called as the base of the cuboid. The four faces which meet the base are called the lateral faces of the cuboid.
In Figure (1) above, EFGH represents the base of a cuboid.
Edges:
The edge of the cuboid is a line segment between any two adjacent vertices.
There are 12 edges, they are AB,AD,AE,HD,HE,HG,GF,GC,FE,FB,EF and CD and the opposite sides of a rectangle are equal.
Hence, AB=CD=GH=EF,AE=DH=BF=CG and EH=FG=AD=BC.
Vertex:
The point of intersection of the 3 edges of a cuboid is called vertex of a cuboid.
A cuboid has 8 vertices A,B,C,D,E,F, G and H represents vertices of cuboid in fig 1.
By observation, the twelve edges of a cuboid can be grouped into three groups such that all edges in one group are equal in length so there are three distinct groups and the groups are named as length, breadth and height.
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Surface Area Of A Cuboid
The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.
Consider a cuboid having length is ‘l’ cm, breadth is ‘b’ cm and height ‘h’ cm.
Area of face EFGH = Area of Face ABCD = (l×b)cm^{2}
Area of face BFGC = Area of face AEHD = (b×h)cm^{2}
Area of face DHGC = Area of face ABFE = (l×h)cm^{2}
Total surface area of a cuboid = Sum of the areas of all its 6 rectangular faces
= 2(l × b) + 2(b × h) +2(l × h)
= 2(lb + bh +lh)
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Lateral Surface Area/ Curved Surface Area Of Cuboid
The sum of surface areas of all sides except top and bottom face of solid is defined as lateral surface area of a solid.
Consider a Cuboid of length,breadth and height to be l, b and h respectively.
Lateral surface area of the cuboid
= Area of face ADHE + Area of face BCGF + Area of face ABFE + Area of face DCGH
=2(b × h) + 2(l × h)
=2h(l + b)
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Solved Examples
Question 1: The length, breadth and height of cuboid shape room are 5m, 4m and 3m respectively. Find the lateral surface area of room
Solution: The given things are
Length = 5m
Breadth = 4m
Height = 3m
Lateral surface area = 2H [L + B]
L.S.A. of cuboid (room) = 2 X 3 [5 + 4]
L.S.A. of cuboid (room) = 6 [9]
L.S.A. of cuboid (room) = 6 X 9
L.S.A. of cuboid (room) = 54m^{2}
Question 2: The length, breadth and height of cuboid shape hall are 15m, 20m and 25m respectively. Find the lateral surface area of hall
Solution: The given things are
Length = 15m
Breadth = 20m
Height = 25m
Lateral surface area = 2H [L + B]
L.S.A. of cuboid (hall) = 2 X 25 [15 + 20]
L.S.A. of cuboid (hall) = 50 [35]
L.S.A. of cuboid (hall) = 50 X 35
L.S.A. of cuboid (hall) = 1750m^{2}
Get Formula Of Total, Curved, Lateral Surface Area: Surface Area Of Cylinder
Question 3: The length, width and height of a cuboid are 10cm, 8cm and 7cm respectively. Find the lateral surface area of a cuboid.
Solution:
Lateral surface area of cuboid is given by:
LSA = 2h(l+w)
where,
l = length = 10 cm
w = width = 8 cm
h = height = 7 cm
Insert these values into the formula we will get:
LSA = 2 ×7(10 + 8)
LSA = 14 × 18
LSA = 252 cm^{2}
Question 4: The length, breadth and height of a cuboid are 16cm, 14cm and 10cm respectively. Find the total surface area of the cuboid.
Solution:
The total surface area of a cuboid is given by:
TSA = 2 (l*b + b*h + h*l)
Given that:
l = 16cm
b = 14cm
h = 10cm
Substituting the values in the equation we will get
TSA = 2 (16*4 + 14*10 + 10*16)
TSA = 2(224 + 140 + 160)
TSA = 2 * 524
TSA = 1048 cm^{2}
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With the help of Surface Area of Cuboid Formula, you can easily solve most of the questions based on Cuboid. Through the above solved examples, you will get the direct idea about the difficulty level of section. Use some tips and tricks to solve questions based on formulas.
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