Surface area of cuboid

 Surface Area of Cuboid

• In everyday life, we have seen many objects like a wooden box, a matchbox, a tea packet, a chalk box, a dice, a book, etc are encountered. 
• All these objects have a similar shape. In fact, all these objects are made of six rectangular planes or square planes.
• In Mathematics, the shape of these objects is either a cuboid or cube.

Definition:

• Imagine objects like a lunch box, television set, shoebox, carton box, bricks, book, mattresses and you would know what a cuboid is and how it looks.
• These shapes are cuboid. Like said, a cuboid is a 3-D geometrical object which consists of 6 rectangular faces.
• All angles of a cuboid are right angles and faces opposite to each other are equal. A cuboid is also known as a rectangular solid or a rectangular prism.
• In a cuboid, the length, width and height may be of different measurements.

Is Cube a Cuboid?

• Objects such as Rubik’s cube, ice, dice, Sudoku, sugar cubes, casseroles and milk crates etc are examples of another 3 dimensional shape called a cube.
• Factually, a cube is a unique form of cuboid in which all sides are similar and squares.

Best Way to Identify a Cuboid

• In a cuboid, each face is in the form of a rectangular shape and the corners or the vertices are 90-degree angles.
• Also, if the opposite faces are always equal to one another then it’s a cuboid.
• For example, a mattress is a cuboid. It consists of 6 surfaces of which each opposite pair is of similar dimensions.

Volume of Cuboids

We can simply find the volume of a cuboid by multiplying the base area with the height. Thus,
volume of cuboid (V) = A  x h
or simply
V = l × b × h

DIAGONALS OF CUBOID

Total Surface Area of Cuboid

If l is the length, b is the breadth and h is the height of a given cuboid, then the sum of areas of 6 rectangles of a cuboid provides the TSA of the cuboid.

Total Surface Area of Cuboid Formula

TSA of cuboid formula = 2 (lw + wh + hl)
Where,
L = length
W= width b= breadth
H = height

Lateral Surface Area Of Cuboid

The sum of the area of 4 side faces i.e. leaving the top and the bottom face provides the LSA of a cuboid. An example of the LSA is the sum of the area of the four walls of a room.

Lateral Surface Area of Cuboid Formula

LSA of cuboid formula = 2 (lh + wh) = 2 h (l + w)
Or simply, 2 (l+w)h
Where,
L = length
W= width or b= breadth
H = height

Solved Examples on Surface Area of Cuboid

Example 1:

The length, width and height of a cuboid are 11cm, 9cm and 15cm respectively. Calculate the total surface area of the cuboid.

SOLUTION:

TSA of a cuboid is given by:  2 (l*w + w*h + w*l)

Given that:

l = 11cm

w = 9cm

h = 15cm

By substituting the values in the expression we will obtain,

TSA = 2 (11*9 + 9*15 + 15*11)

TSA = 2(99 + 135 + 165)

TSA = 2 * 399

TSA = 798cm²

Example 2:

Find out the lateral surface area of a cube having an edge of 20cm?

 

Solution:

We know that the LSA of a cuboid is given by 2(l+b)h
Now, since a cube is also a cuboid in which l=b=h=a, thus LSA of a cube = 2(a+a)
Or simply,
a = 4a2

 

Formula for Lateral Surface Area of Cube = 4a2

Given that a = 20 cm.

Therefore,

LSA = 4(202) = 1600 cm2

Properties

• A Cuboid is made up of six rectangles, each of the rectangles is called the face.
• The edge of the cuboid is a line segment between any two adjacent vertices.
• The point of intersection of the 3 edges of a cuboid is called the vertex of a cuboid.

Fun Facts

• It has 12 edges.
• It has 8 corners or vertices.
• It has 6 faces.

Cuboid Examples

The textbooks we read, the lunch box we carry to school, the mattresses on which we sleep, and the bricks we use to construct a house, etc., are well-known examples of a cuboid present in our environment.