Cuboid Surface Area

Cuboids are three dimensional objects that are made up of mainly solid substances. The cuboids are six faced objects where the faces have independent dimensions and values. In quantitative aptitude we basically work with the data of a certain parameter in any specific context. As said earlier the cuboid is a six faced object it actually has numerous data of all the faces and with the different data we have to calculate the surface area of the cuboid. The physical measurement of the surface area of a cuboid is not possible. To do the task we generally make calculations of different planes and then do summation, deletion and multiplication. 

Definition for “Surface Area of Cuboid”

Surface area is a two dimensional calculated amount of any solid or liquid object exposed to naked eyes. The amount of area any object is consuming at a constant time is called the surface area of that object.

Definition for “Total Surface Area of a Cuboid”

The total surface area of a cuboid is basically the amount of area covered by a cuboid. Being a three dimensional solid with three pairs of equal dimensional planes to calculate the area we used to calculate all the surface areas of all the planes and then add them. But it is not an easy and suitable process to do mathematically. Then here we take the help of Arithmetics to resolve the big problems. There in the real world we used to calculate the two kinds of surface area of a cuboid. The two types are termed as total surface area of cuboid, and lateral surface area of cuboid. 

Formula for Total Surface Area of a Cuboid 

The total surface area of a cuboid with three dimensions can be calculated by the formula mentioned below.

Total Surface Area of Cuboid = 2 (l*w + w*h + l*h)

• L for the length of the cuboid,
• H for the height of the cuboid,
• W for the width of the cuboid 

The calculations are done in this way because all faces connect with each other in alternative planes and form different surfaces and the surfaces are exposed to the naked eyes and then summation of all the surface areas of all the planes are equal so it makes the value of total surface area of cuboid.

Definition for Lateral Surface Area of a Cuboid

The lateral surface area of a cuboid is actually the summation of all the surface areas of the vertical faces of the cuboid.

Formula for Lateral Surface Area of a Cuboid 

If we consider the parameters of the total surface areas then by going into that standard we can calculate the lateral surface area of the cuboid is:

Lateral Surface Area = Total Surface Area – Area of top and bottom faces

 Lateral Surface Area = 2 (l*w + w*h + l*h) – (2 * l * w)

= 2*l*w + 2*w*h + 2*l*h – 2*l*w

= 2*l*h + 2w*h

= 2*h*(l + w)

From the above formula we can get that we consider all the planes which are vertical on the plane. Not considering the planes respectively touching the ground and having no touch to the ground. 

Examples of total surface and lateral surface area of a cuboid

Example 1: A cuboid has a dimension of 3 cm width, 6 cm length, and 8 cm height. Then calculate the total surface area of a cuboid.

Solution:  Let’s say a cuboid of 3 cm. width, 6 cm. length and 8 cm. Height. 

The total area of the cuboid will be

= 2*(l*w+ l*h+h*w)

= 2 *(3*6+6*8+8*3)

= 2*(18+48+24)

= 2*90

=180 sq. cm

Example 2: 

Find the lateral surface area of a cuboid whose length is 5 cm, width is 3 cm, and height is 2 cm.

Solutions: 

Here we get that l = 5 cm, w = 3 cm, and h = 2 cm

Then according to the formula the lateral surface area can be calculated as 

2 (l*w + w*h + l*h) – (2*l*w)

= 2 (5*3+3*2+5*2)-(2*5*3)

=2 (15 + 6 +10)-(30)

= 2*(31)-30

= 62-30

=32 sq. cm.

Conclusion 

In this project one is generally focused on doing the day to day task of area calculation of a cuboid. The types of the areas of a cuboid is distinguishably done here. The definition of all the parameters and facts are extrapolated and done in simple languages. Scientific outlooks on surface area and the reasons behind the formulations have been discussed. The logic is also given as an important fact of this workout. Here the differences of two different kinds of cuboid their importance and their definition is given. There we made proper formulation of both the types and made them understandable by giving examples and making solutions of each problem of both types.