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119 LearnersLast updated on August 30, 2025
Surface Area of Rectangular Cube
A rectangular cube, also known as a rectangular prism, is a 3-dimensional shape with six rectangular faces. The surface area of a rectangular cube is the total area covered by its outer surfaces. This includes the areas of all six rectangular faces. In this article, we will learn about the surface area of a rectangular cube.
What is the Surface Area of a Rectangular Cube?
The surface area of a rectangular cube is the total area occupied by the boundary or surface of the cube. It is measured in square units.
A rectangular cube, or rectangular prism, has three pairs of opposite rectangular faces.
Each pair of faces has the same dimensions, making it a uniform shape.
The surface area of a rectangular cube includes the areas of all six faces.
Surface Area of a Rectangular Cube Formula
A rectangular cube has six faces, and its surface area is calculated by summing the areas of all the faces.
The formula for the surface area of a rectangular cube is given as:
Surface Area = 2(lw + lh + wh) square units
Here, l is the length, w is the width, and h is the height of the rectangular cube.
Example Calculation
To calculate the surface area of a rectangular cube, we use the formula:
Surface Area = 2(lw + lh + wh)
Assume a rectangular cube with length 5 cm, width 3 cm, and height 4 cm.
The surface area is: Surface Area = 2(5×3 + 5×4 + 3×4) = 2(15 + 20 + 12) = 2×47 = 94 cm²
Volume of a Rectangular Cube
The volume of a rectangular cube shows how much space is inside it. It tells us the capacity or the amount it can hold.
The volume of a rectangular cube is found by using the formula:
Volume = l×w×h cubic units
Where l is the length, w is the width, and h is the height of the cube.
Confusion between formulas for different shapes
Students might confuse the formula for the surface area of a rectangular cube with formulas for other shapes like cylinders or spheres. Always remember the formula:
Surface Area = 2(lw + lh + wh).
Mistake 1
Using incorrect dimensions
Some students mistakenly use incorrect dimensions for length, width, or height. Double-check your measurements before substituting them into the formula.
Mistake 2
Calculating only one face
A common mistake is calculating the area of only one face and forgetting to account for all six faces. Ensure you use the formula that adds up all the faces: 2(lw + lh + wh).
Mistake 3
Incorrect multiplication or addition
Errors in basic multiplication or addition can lead to incorrect results. Break down the calculation into steps and verify each step to avoid mistakes.
Mistake 4
Solved Examples of Surface Area of Rectangular Cube
Find the surface area of a rectangular cube with a length of 7 cm, width of 4 cm, and height of 3 cm.
Surface Area = 94 cm²
Problem 1
Given l = 7 cm, w = 4 cm, h = 3 cm. Use the formula: Surface Area = 2(lw + lh + wh) = 2(7×4 + 7×3 + 4×3) = 2(28 + 21 + 12) = 2×61 = 122 cm²
Find the volume of a rectangular cube with a length of 5 cm, width of 3 cm, and height of 2 cm.
Explanation
Volume = 30 cm³
Problem 2
Use the formula: Volume = l×w×h = 5×3×2 = 30 cm³
A rectangular cube has a surface area of 150 cm². If its length is 5 cm and width is 3 cm, find its height.
Explanation
Height = 5 cm
It is the total area that covers the outside of the rectangular cube, including all six rectangular faces.
1.How do you calculate the surface area of a rectangular cube?
2.What unit is surface area measured in?
3.What is the volume of a rectangular cube?
4.Are all faces of a rectangular cube equal?
Common Mistakes and How to Avoid Them in the Surface Area of a Rectangular Cube
Students often make mistakes while calculating the surface area of a rectangular cube, which leads to wrong answers. Below are some common mistakes and ways to avoid them.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
