How To Find Lateral Surface Area Of Cuboid
A cuboid is a 3-dimensional figure divisional by 6 rectangular planes, having a unlike magnitude of length, width and meridian. If you look around and y'all can see a box, brick or annihilation in the shape of a rectangle, it could be cuboid. A cuboid (3-dimensional) can exist seen made up of rectangles (2-dimensional) of different dimensions when seen from any of the ends. In this article, we are going to discuss the definition of cuboid, total and lateral surface area of a cuboid in a detailed mode.
Tabular array of Contents:
- Cuboid Definition
- Surface Area of Cuboid Formula
- Total Area
- Lateral Expanse
- Total Area of a Cuboid Derivation
- Examples
- FAQs
Cuboid Definition
A cuboid is a iii-dimensional effigy or solid which has six rectangular sides called faces. Each face of a cuboid is a rectangle and all of its corners are ninety-degrees. It has 8 vertices and 12 edges. The opposite faces of a cuboid are always equal. It means that the contrary surfaces of the cuboid are in the same dimension. The measures of the cuboid are the Total Surface Area (TSA), Lateral or curved Surface area (CSA) and volume. The surface areas are measured in terms of square units, whereas the volume of the cube is measured in terms of cubic units.
Expanse of Cuboid
The area of a cuboid refers to the surface expanse as the cuboid is a three dimensional solid. Thus, the expanse of cuboid can be calculated using the formula of area of rectangle , since the faces of a cuboid are in a rectangular shape.
Cuboid Surface Expanse
The surface area of the cuboid can be of ii types-
(i) Full Surface Expanse
(ii) Lateral Surface Expanse or Curved Expanse
Surface Area of Cuboid Formula
Before going into the concept of area, allow us denote the dimensions of a cuboid, which are,
Length, Width, and Peak are represented by l, west, h, respectively.
Full Surface Area of a Cuboid
The Total surface area of a cuboid (TSA) is equal to the sum of the areas of it's 6 rectangular faces, which is given past:
Total Surface Area of a Cuboid (TSA) = two (lw + wh + lh) square units
The to a higher place formula gives the total surface surface area of a cuboid having all half dozen faces.
Lateral Surface Surface area of a Cuboid
The lateral surface area of a cuboid is the sum of four planes of a rectangle, leaving the top (upper) and the base of operations (lower) surface. Mathematically, the Lateral Area of a cuboid (LSA) is given equally:
Lateral Surface area of a cuboid (LSA) = 2 (lh + wh) = ii h (l + w) square units
Also, acquire:
- Cuboid and Cube
- Volume of a Cuboid
- Surface area and Volumes
- 3D shapes
- Difference Between Cube and Cuboid
Total Area of a Cuboid Derivation
As the cuboid has 6 rectangular faces, the full expanse of the cuboid is calculated as follows:
Assume that, fifty, w, h exist the length, width, and height of the cuboid respectively.
Thus,
The front end face expanse of cuboid = 50 x h
The back face surface area of the cuboid = l x h
The top face area of the cuboid = l x westward
The bottom confront area of the cuboid = l ten w
The left face expanse of the cuboid = h x w
The right face area of cuboid = h ten w
Hence, the full surface surface area is the sum of all the faces of a cuboid, then the TSA of a cuboid is:
Total Surface Area of Cuboid = lh + lh + lw+ lw+ hw+ hw
Total Area of Cuboid = 2 lh + 2 lw + 2 hw
Total Surface Surface area of Cuboid = 2 (lh + lw+ hw)
Therefore, the total surface surface area of the cuboid is two (lh + lw+ hw) square units.
Surface Area of Cuboid Example
Instance 1:
Given below is a cuboid having its dimension given every bit length = 8 cm, width = 6 cm and height = five cm, find the TSA of a cuboid.
Solution
Given:
h = 5 cm
w = half dozen cm
l = 8 cm
Using the formula: TSA = 2 (lw + wh + hl)
2( (8×six) + (6×five) + (five×8))
= two(48 + 30 + 40)
= 2(118)
= 236
So, the full surface surface area of this cuboid is 236 cm².
Example 2:
The dimensions of a cuboid are given as follows:
Length = 4.8 cm
Width = iii.4 cm
Height = 7.two cm.
Find the Total Area and the Lateral Surface area.
Solution:
The total expanse is given equally
TSA = 2 (lw + wh + hl)
=2((iv.viii ×3.four) + (3.4×7.2) + (7.2×4.viii))
= two(16.32 +24.48 +34.56)
= 2(75.36) cm²
Therefore, TSA of a cuboid= 150.72 cm
Also, the lateral surface expanse = 2 h (l + w)
= 2×7.2 (4.eight + 3.iv)
= 14.iv (8.2) = 118.08
Therefore, LSA of a cuboid = 118.08 cm²
Learn more about various geometrical figures, surface areas and volumes by visiting our site BYJU'S – The Learning App.
Frequently Asked Questions on Surface Area of Cuboid
What is the area of the cube and cuboid?
The surface area of the cube tin can be found using the formulas given below:
LSA = 4a^2
TSA = 6a^2
The expanse of the cuboid tin can be found using the formulas given beneath:
LSA = 2h(fifty + b)
TSA = 2(lb + bh + hl)
What is the latest area of a cuboid?
The lateral surface surface area of a cuboid is the expanse of four faces other than top and bottom. The formula to discover the lateral surface area is:
LSA = 2h(l + b)
How do yous find the surface area and volume of a cuboid?
The area, i.e. the full surface expanse of a cuboid is the sum of areas of all the faces and the formula is given by:
Surface surface area of cuboid = 2(lb + bh + hl)
The volume of the cuboid is calculated using the formula:
Book = lbh
What is the total surface area and lateral surface expanse?
The full surface surface area of any solid refers to the sum of areas of all the faces, whereas the lateral area refers to the area of walls, i.e.eastward the faces other than top and bottom faces.
What is the divergence between total expanse and the curved surface expanse?
The primary deviation between the total expanse (TSA) and curved surface area (CSA) is that TSA refers to the surface area of all the faces of the solid, whereas the CSA is the area of the curved region of the solid and this excludes the areas of summit and bottom regions.
Source: https://byjus.com/maths/surface-area-of-cuboid/
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