Area of Cuboid
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.
What is the 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
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
Example 3:
Williams built a rectangular cardboard box 20 cm high. It has a square base and a volume of 2000 cm³. Then he realized that he did not require a box that elongated, so he cut short the height of the box decreasing its volume to 1,000 cm³. Find out the height of the new box and is the new box cubicle?
Solution:
Volume of cuboid (V) = length × width × height = Base area × height.
Given that,
V = 2000 cm³,
height = 20 cm
Substituting the values in the formula, we obtain
Base area = 2000/20 = 100 cm²
We also know that the base of this box is a square.
Thus, it indicates that the length = width.
Hence, the length of square base = √100 = 10 cm
After shortening of height, new volume = 1000
= 10 ×10 x new height
Thus, new height = 1000/ 10 × 10 = 10 cm
As all the dimensions of the solid, l, w, h measure similar, the resulting solid is also a cube.
FAQs on Surface Area of Cuboid
Q1. What is the Diagonal of a Cuboid?
Answer: The length of the longest diagonal of a cuboid is given as:
Length of diagonal of cuboid = √ (l² + b² + h²), where l= length, b= breadth, h= height
Q2. What are the Properties of a Cube Number?
Answer:
Cubes of positive numbers are positive invariably.
For example, cube of +3 is = (+3) × (+3) × (+3) = +27
Cubes of positive numbers are invariably negative.
For example, cube of -3 is = (-3) × (-3) × (-3) = -27
Cubes of even numbers even invariably.
Cubes of odd numbers are odd invariably.
Q3. How Do We Measure the Volume of Water?
Answer: Generally, it is not feasible to measure the volume of water until it is stored in a container, which can be a cube, cuboid, cone, cylinder, and cone etc. And once it is inside a container we need to compute the volume of the container in order to ascertain the volume of water.
Q4. What is Meant by Nets of a Cuboid?
Answer: Another way to have a perception of the surface area of a cuboid is to take into account a net of the cuboid. The net is a 2-D geometrical shape that can be molded to create a 3-D object.
Imagine cutting along some edges of a cuboid and opening it up to create a plane figure. The plane figure is what we call the net of the cuboid.
