How to Calculate Area of a Cube

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Calculating the area of a cube is an essential mathematical skill that is frequently used in geometry and everyday life. A cube is a three-dimensional shape with six square faces, and its area can be determined by finding the sum of the areas of all its faces. This calculation plays a vital role in numerous fields, such as architecture, engineering, and construction, where precise measurements are required to determine the amount of materials needed or to understand the proportions of a three-dimensional object. In this guide, we will explore the step-by-step process of calculating the area of a cube, providing clear explanations and examples to ensure a comprehensive understanding of this fundamental concept in geometry. Whether you are a student learning geometry or simply have an interest in exploring the mathematical properties of three-dimensional shapes, this guide will equip you with the necessary knowledge and skills to confidently calculate the area of a cube.

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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

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The surface area of an object is the sum of the areas of the faces on the object. The cube has 6 equal faces, so all you need to do is calculate the area of one face and multiply it by 6. See the article below to determine the area of a cube.

Table of Contents

Steps

Find the area when the length of one side is known

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Area of a cube formed by 6 faces. Since all the faces of the cube are equal, we just need to find the area of one face and multiply it by 6 to get the total area. The surface area is calculated using the simple formula: 6 xs ² , where “s” is the side of the cube. ^{[1] X Research Source}

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Find the area of one face of the cube. To find the area of a cube’s face, you need to find the “s” or side lengths of the cube, and then calculate s ² . In other words, you would multiply the length times the width (in a cube the two lengths are equal). For example, if the side of the cube is 4 cm or s = 4 cm, the area of one face of the cube will be (4 cm) ² = 16 cm ² . Remember to write your answer in units of area. ^{[2] X Research Source}

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Multiply the area of one face by 6. Once you find the area of one face of the cube, simply multiply this by 6. We have: 16 cm ² x 6 = 96 cm ² . So the area of the cube is 96 cm ² . ^{[3] X Research Sources}

Calculate the area when the volume is known

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Determine the volume of the cube. For example, the volume of a cube is 125 cm ³ . ^{[4] X Research Sources}

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Find the cube root of the volume. To find the cube root of the volume, you just need to determine the number that when cubed up equals the volume (or use a calculator). This number is not always an integer. In the example with a volume of 125 cm ³ , this is a perfect cube whose square root is 5, because 5 x 5 x 5 = 125. So the length of the “s” side of the cube is 5. ^{[5] X Research Source}

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Substitute this result into the formula for the area of a cube. Once you find the side lengths, you just need to substitute the formula for the area of the cube: 6 xs ² . Since s = 5 cm, we have: 6 x (5 cm) ² .

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Calculate the final result. So the area of the cube is 6 x (5 cm) ² = 6 x 25 cm ² = 150 ² .

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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

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This article has been viewed 12,022 times.

The surface area of an object is the sum of the areas of the faces on the object. The cube has 6 equal faces, so all you need to do is calculate the area of one face and multiply it by 6. See the article below to determine the area of a cube.

In conclusion, calculating the area of a cube is a simple and straightforward process. By using the formula A = 6s^2, where A represents the area and s represents the length of a side, one can easily determine the surface area of a cube. This formula is valid for all cubes regardless of their size. Additionally, understanding the concept of surface area is crucial in various fields such as mathematics, engineering, and architecture, as it provides important information about the cube’s exterior. By following the steps outlined in this guide, anyone can easily and accurately calculate the area of a cube, making it a useful tool for solving real-life problems and applications.

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