Surface Area of Rectangular Cube
2026-02-28 00:50 Diff

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Last updated on August 30, 2025

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

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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).

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

Okay, lets begin

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

Well explained 👍

Problem 2

Use the formula: Volume = l×w×h = 5×3×2 = 30 cm³

Okay, lets begin

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

Well explained 👍

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?

Use the formula: Surface Area = 2(lw + lh + wh), where l, w, and h are the dimensions of the cube.

2.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

3.What is the volume of a rectangular cube?

The volume is the amount of space inside the cube, calculated by the formula Volume = l×w×h.

4.Are all faces of a rectangular cube equal?

No, a rectangular cube has pairs of opposite faces that are equal, but not all six faces are necessarily equal unless it's a cube.

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