103 LearnersLast updated on August 30, 2025
Surface Area of Cubes and Rectangular Prisms
Cubes and rectangular prisms are 3-dimensional shapes with flat faces. The surface area of these shapes is the total area covered by their outer surfaces. For cubes, all faces are equal squares, while rectangular prisms have opposite faces that are equal rectangles. In this article, we will learn about the surface area of cubes and rectangular prisms.
What is the Surface Area of Cubes and Rectangular Prisms?
The surface area of cubes and rectangular prisms is the total area occupied by the boundary or surface of these shapes.
It is measured in square units.
A cube is a 3D shape with all sides equal, making it a special type of rectangular prism.
A rectangular prism has six rectangular faces, with opposite faces being identical.
Surface areas are classified based on the shape: the surface area of a cube and the surface area of a rectangular prism.
Surface Area of Cubes and Rectangular Prisms Formula
Cubes and rectangular prisms have straightforward surface area formulas due to their regular shapes.
For a cube with side length s, the surface area is:
Surface Area of a Cube = 6s²
For a rectangular prism with length l, width w, and height h, the surface area is:
Surface Area of a Rectangular Prism = 2(lw + lh + wh)
Surface Area of a Cube
The surface area of a cube is the total area covered by all six of its identical square faces.
Each face of a cube is a square with the side length s.
The formula to calculate the surface area of a cube is:
Surface Area = 6s² Where s is the length of a side of the cube.
Surface Area of a Rectangular Prism
The total area occupied by the rectangular prism, including the area of all six rectangular faces, is known as the surface area of the rectangular prism.
The formula for calculating the surface area is:
Surface Area = 2(lw + lh + wh)
Where l is the length, w is the width, and h is the height of the rectangular prism.
Volume of Cubes and Rectangular Prisms
The volume of these shapes shows how much space is inside them.
For a cube, the volume is the cube of its side length, and for a rectangular prism, it’s the product of its dimensions.
The formulas are:
Volume of a Cube = s³ Volume of a Rectangular Prism = lwh
Confusing volume with surface area
Students sometimes mix up the concept of volume and surface area. Remember, volume measures the space inside, while surface area measures the outer covering.
Mistake 1
Using incorrect formulas
Ensure you use the correct formula for the shape. For cubes, use 6s², and for rectangular prisms, use 2(lw + lh + wh).
Mistake 2
Incorrectly identifying dimensions
Students may mix up the dimensions of length, width, and height. Always clearly identify each dimension to apply the formula correctly.
Mistake 3
Misplacing parentheses in calculations
When calculating the surface area of a rectangular prism, ensure the correct use of parentheses to avoid miscalculations in the formula 2(lw + lh + wh).
Mistake 4
Assuming all rectangular prisms are cubes
Some students mistakenly apply the cube’s formula to all prisms. Remember, a cube is a special type of prism with all sides equal.
Mistake 5
Solved Examples of Surface Area of Cubes and Rectangular Prisms
Find the surface area of a cube with a side length of 4 cm.
Surface Area = 96 cm²
Problem 1
Given s = 4 cm. Use the formula: Surface Area = 6s² = 6 × (4)² = 6 × 16 = 96 cm²
Find the surface area of a rectangular prism with dimensions 3 cm by 4 cm by 5 cm.
Explanation
Surface Area = 94 cm²
Problem 2
Use the formula: Surface Area = 2(lw + lh + wh) = 2(3 × 4 + 3 × 5 + 4 × 5) = 2(12 + 15 + 20) = 2 × 47 = 94 cm²
A cube has a side length of 7 cm. Find its surface area.
Explanation
Surface Area = 294 cm²
Problem 3
Use the formula: Surface Area = 6s² = 6 × (7)² = 6 × 49 = 294 cm²
Find the surface area of a rectangular prism with length 10 cm, width 4 cm, and height 6 cm.
Explanation
Surface Area = 248 cm²
Problem 4
Use the formula: Surface Area = 2(lw + lh + wh) = 2(10 × 4 + 10 × 6 + 4 × 6) = 2(40 + 60 + 24) = 2 × 124 = 248 cm²
The surface area of a cube is 150 cm². Find the side length.
Explanation
Side Length = 5 cm
It is the total area that covers the outside of the cube across all six of its equal square faces.
1.How do you calculate the surface area of a rectangular prism?
2.What is the difference between a cube and a rectangular prism?
3.Are surface area and volume the same?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of Cubes and Rectangular Prisms
Students often make mistakes while calculating the surface area of cubes and rectangular prisms, leading to incorrect answers. Below are some common mistakes and the ways to avoid them.
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
