Surface Area of Cuboid

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.