Total Surface Area of Cuboid: Comprehensive Overview
A cuboid's surface area is the total space filled by all of its surfaces/sides. A cuboid is a three-dimensional form with six rectangular sides. A cuboid, also known as a regular hexahedron, is a regular hexahedron with six rectangular faces, eight vertices, and twelve edges with congruent, opposite faces. It is a three-dimensional rectangle with four lateral sides and two top and bottom faces. Bricks, geometric boxes, shoe boxes, packing boxes, and other cuboids are commonplace.
Total Surface Area of Cuboid: What is a Cuboid?
A cuboid is a three-dimensional shape or solid with six rectangular faces. A cuboid's faces are rectangles, and all of its corners are 90 degrees. It has eight vertices and twelve edges. A cuboid's opposing faces are always equal. It signifies that the cuboid's opposed surfaces are in the same dimension. The cuboid's measurements are Total Surface Area (TSA), Lateral or Curved Surface Area (CSA), and volume. The surface areas of cubes are measured in square units, whereas the volume is measured in cubic units.
Total Surface Area of Cuboid: What is the Surface Area of Cuboid?
The surface area of a cuboid is the entire area covered by all of its surfaces, and because the cuboid is the 3-D form of a rectangle, the height of the cuboid is also involved in determining the surface area. In 3-D figures, surface area and volume are determined. A cuboid's surface area is measured in square units (for example, cm2, m2, etc).
Total Surface Area of Cuboid: What is Cuboid Surface Area?
The cuboid's surface area can be of two types-
- Total Surface Area
- Lateral Surface Area or Curved Surface Area
Read more about the Formula of the CSA of Cylinder.
Total Surface Area of Cuboid: Cuboid Formula?
Before delving into the idea of the area, consider the dimensions of a cuboid-
The letters l, w, and h stand for length, width, and height, respectively.
Total Surface Area of Cuboid
A cuboid's total surface area (TSA) is equal to the sum of the areas of its six rectangular sides, which is given by-
Total Cuboid Surface Area (TSA) = 2 (lw + wh + lh) square units.
The formula above calculates the total surface area of a cuboid with all six faces.
Lateral Surface Area of Cuboid
A cuboid's lateral surface area is the total of the four planes of a rectangle, except the top (upper) and bottom (lower) surfaces. The Lateral Surface Area (LSA) of a cuboid is given mathematically as-
Lateral Surface Area (LSA) = 2 (lh + wh)
= 2 h (l + w) square units.
Total Surface Area of Cuboid: Derivation of the Total Surface Area of Cuboid
Because the cuboid has six rectangular sides, its total surface area is determined as follows-
Assume that l, w, and h are the cuboid's length, breadth, and height, respectively.
Thus,
The area of cuboid's front face = l x h
The area of cuboid's rear face region = l x h
The area of cuboid's upper face region = l x w
The area of cuboid's bottom face region = l x w
The area of cuboid's left face region = h x w
The area of cuboid's right face region = h x w
As the total surface area of a cuboid equals the sum of all its faces, the TSA of a cuboid is-
Total Surface Area of Cuboid = lh + lh + lw+ lw+ hw+ hw
Total Surface Area of Cuboid = 2 lh + 2 lw + 2 hw
Total Surface Area of Cuboid = 2 (lh + lw+ hw)
As a result, the cuboid's total surface area is 2 (lh + lw + hw) square units.
Total Surface Area of Cuboid: How to Calculate the Surface Area of a Cuboid?
The surface area of a cuboid is the entire area of the cuboid's sides/surfaces. The following are the steps below to figure out how to get the surface area of a cuboid-
Step 1: Examine and record the measurements of each size. If the dimensions have multiple units, combine them into one.
Step 2: Calculate the total surface area of the cuboid using the formula TSA = 2 (lb + bh + lh) square units.
Step 3: Make a note of the area included in the appropriate units.
Total Surface Area of Cuboid: Sample Example for the Calculation of the Total Surface Area of a Cuboid
Determine the total surface area and lateral surface area of a cuboid with dimensions of 9 inches in length, 3 inches in width, and 5 inches in height.
Solution: In this case, Length (l) = 9 inches
Width (w) = 3 inches
Height (h) = 5 inches.
Total Surface Area of Cuboid = 2 (lw + wh + lh)
= 2 [(9 x 3) + (3 x 5) + (5 x 9)]
= 2 [27 + 15 + 45]
= 2 x 87
= 174 in²
Lateral surface area of Cuboid = 2 h(l + w)
= (2 x 5) (9 + 3)
= 270 in2
Read more about the Perimeter of Cuboid and the Volume of Cuboid Formula.
Total Surface Area of Cuboid: Difference between TSA and CSA of Cuboid
The fundamental difference between TSA and CSA of the cuboid is that TSA covers all six cuboid faces, whereas CSA only includes the cuboid's vertical faces. TSA measures the overall area of the cuboid that must be covered or painted, whereas CSA measures the area of the curved surface that wraps around the cuboid. The table below details the differences between the cuboid's total surface area and curved surface area-
Read more about the Difference Between Cube and Cuboid.
Total Surface Area of Cuboid: Uses of Surface Area of Cuboid
The surface area of a cuboid has several real-world applications in engineering, building, manufacturing, architecture, and other industries. Here are a few uses of the total surface area of cuboids-
- Heat transmission: The surface area of a cuboid is also used to measure the rate of heat transmission in a solid object; hence, a material's surface area is an important factor in its thermal conductivity.
- Manufacturing: The surface area of cuboids is used in manufacturing to calculate the quantity of material required to construct a product.
- Packaging: Knowing the surface area of a cuboid may assist businesses in determining the quantity of material needed and ensuring that the product fits correctly inside the packaging.
- Painting: Knowing how much paint is needed to cover a rectangular box or cuboid is essential for painters when estimating the cost of paint for a job.