Cuboid Surface Area: Formula, Definition, Examples, and Frequently Asked Questions
A cuboid's surface area is the total amount of space it takes up. A cuboid is a six-faced three-dimensional shape with each face shaped like a rectangle. Let us learn more about the surface area of a cuboid formula and solve problems based on the surface area of a cuboid.
What is the Cuboid's Surface Area?
A cuboid's surface area is the sum of all its surfaces. Because a cuboid is a three-dimensional solid shape, the value of its surface area is determined by its length, width, and height. The value of a cuboid's surface area changes when any of its dimensions change. A cuboid's surface area is measured in square units.
Cuboid Surface Area Formula
The formula for a cuboid's surface area is determined by the type of surface area requested. There are two types of surface areas on a cuboid:
- Surface Area Total
- Surface Area on the Lateral Side
The total surface area of the cuboid is calculated by adding the areas of all six faces, whereas the lateral surface area of the cuboid is calculated by calculating the areas of each face excluding the base and top. A cuboid's total surface area and lateral surface area can be expressed in terms of length (l), width (w), and height (h) as:
Total Cuboid Surface Area = 2 (lw wh lh)
Cuboid Lateral Surface Area = 2h (l w)
If the surface area is given or requested without any specifics, it refers to the total surface area. By opening a cuboidal box, we can see how to derive the formulas for the surface area of the cuboid.
Cuboid Surface Area Calculation
A cuboid has six rectangle faces. To calculate the total surface area of a cuboid, add the areas of all six rectangular faces.
Cuboid's Total Surface Area
By adding the areas of each face, the total surface area of the six faces can be calculated. Because each face of a cuboid is a rectangle, the area of the rectangle for each face is calculated and added to obtain the cuboid's total surface area. Let us explain this with the help of the diagram below.
As shown in the figure above, all of the faces are numbered 1, 2, 3, 4, 5, and 6. In other words, if we imagine the cuboid as a two-dimensional net, we get this figure.
- Area of Rectangles 1 and 2: This is the area of the top and bottom faces of the rectangle = l w This results in lw lw = 2lw.
- Rectangle 3 and 4 Area: This is the area of the rectangle's front and back faces = w h This results in wh wh = 2wh.
- Rectangle 5 and 6 Area: This is the area of the rectangle formed by the faces on the left and right sides = l h This results in lh lh = 2lh.
As a result, the total surface area of the six faces = 2lw 2wh 2lh
As a result, the total surface area of a cuboid with dimensions l, w, and h is = 2 (lw wh lh).
Cuboid Lateral Surface Area
A cuboid's lateral surface area is the sum of the surface areas of its four vertical faces. If we remove the top and bottom faces from the figure above, we get the area of the cuboid's lateral surface area. The cuboid's lateral surface area is,
Total Surface Area - Top and Bottom Face Area = Lateral Surface Area
2 (lw wh lh) - (2 l w)
= 2lw 2wh 2lh – 2lw
= 2lh 2wh
= 2h(l w)
To illustrate this with a real-world example, imagine a room in the shape of a cuboid. The total surface area of the room will be the sum of the six faces (the four vertical walls, the floor, and the ceiling), whereas the lateral surface area will be the sum of the four vertical walls (the areas of the floor and ceiling are not included). added)
How to Calculate the Surface Area of a Cuboid
The surface area of a cuboid is the total area of each surface of a cuboid. Let us calculate the total surface area of a cuboid using the steps below.
- Step 1: Determine whether or not the cuboids' dimensions are in the same units. If not, convert the measurements to the same units.
- Step 2: Calculate total surface area using the formula = 2(lw wh lh).
- Step 3: To calculate the area, substitute the given values and express it in square units.
With the help of an example, let us learn how to calculate the total surface area and lateral surface area of a cuboid.
Find the total surface area and lateral surface area of a cuboid with dimensions of 6 inches in length, 4 inches in width, and 3 inches in height.
As we know, the total surface area of a cuboid is 2 (lw wh lh), and the lateral surface area is 2h(l w).
In this case, length (l) equals 6 inches, width (w) equals 4 inches, and height (h) equals 3 inches.
Total surface area of the cuboid = 2 (lw wh lh) = 2 [(6 4) (4 3) (6 3)] in2
Cuboid total surface area = 108 in2
Cuboid lateral surface area = 2h(l w) = (2 3)(6 4) in2
Cuboid lateral surface area = 60 in2
As a result, the cuboid's total surface area is 108 in2, and its lateral surface area is 60 in2.
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Example 1: Determine the lateral surface area of a cuboid with dimensions of 20 inches in length, 10 inches in width, and 15 inches in height.
As we know, the lateral surface area of a cuboid is L = 2h(l w), and it follows that
20 in length (l)
width (w) = ten inches
15 in height (h)
Let us change the values in the formula,
Cuboid lateral surface area = 2h(l w)
⇒ 2 × 15(20 10)900 square inches = 30(20 10) 30 (30)
As a result, the cuboid's lateral surface area is 900 square inches.
Example 2: Determine the total surface area of a cuboid that is 8 m long, 5 m wide, and 4 m high.
Solution: Given that the cuboid's length (l) = 8 m, width (w) = 5 m, and height (h) = 4 m
The cuboid's total surface area = 2 (lw wh lh).
So, let us change the values in the formula.
Total cuboid surface area = 2 (lw wh lh) 2 [(8 5) (5 4) (8 4)]
⇒ 2 [40 20 32]
⇒ 2 × 92 = 184 m2
As a result, the cuboid's total surface area is 184 m2.
Example 3: State whether something is true or false.
a A cuboid has seven rectangular faces.
b ) To calculate the total surface area of a cuboid, add the areas of all six rectangular faces.
Solution:
a True, a cuboid has six rectangular faces.
b True, in order to determine the total surface area of a cuboid, we must add the areas of all six rectangular faces.
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Questions and Answers about Cuboid Surface Area
A cuboid's total surface area is the sum of all its surfaces. To calculate the total surface area of a cuboid, add the areas of all six rectangular faces. The total surface area of a cuboid is calculated as 2 (lw wh lh), where l = length, w = width, and h = height of the cuboid.
What is a Cuboid's Lateral Surface Area?
A cuboid's lateral surface area is the value of its surface area excluding its top and bottom surfaces. The formula for a cuboid's lateral surface area is 2h(l w), where l = length, w = width, and h = cuboid height.
What Is the Difference Between a Cuboid's Total Surface Area and Lateral Surface Area?
The difference between a cuboid's total surface area and lateral surface area is given below:
- A cuboid's total surface area is the sum of the areas of all six faces, whereas its lateral surface area is the sum of the areas of faces excluding the top and bottom.
- A cuboid's total surface area is calculated using formula 2(lw wh lh), whereas its lateral surface area is calculated using formula 2h(l w).
What is a Cuboid's TSA and LSA?
A cuboid's TSA and LSA are abbreviations for Total Surface Area (TSA) and Lateral Surface Area (LSA). The total surface area is the sum of the surface areas of all six faces, whereas the lateral surface area excludes the top and bottom faces.
What is the Surface Area of a Cuboidal Box Without a Lid?
There are two ways to calculate the total surface area of a cuboidal box without a lid:
- Method 1: Total surface area of a Cuboidal Box Without Lid = total surface area of the cuboid minus one rectangular face
- Method 2: Total surface area of a Cuboidal Box without a Lid = lateral surface area of a cuboid with one rectangular face
It should be noted that both methods yield the same result.
What is the Cuboid Surface Area Unit?
A cuboid's surface area is measured in square units such as cm2, m2, inch2, and so on.
What is the formula for calculating a cuboid's total surface area?
The formula for calculating the total surface area of a cuboid is 2 (lw wh lh), where l = length, w = width, and h = cuboid height.
What is the formula for calculating a cuboid's lateral surface area?
The lateral surface area of a cuboid is calculated using the formula 2h(l w), where l = length, w = width, and h = height of the cuboid.
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