This article was co-authored by David Jia. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for 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 combined area of all of the sides on its surface. All six sides of a cube are congruent, so to find the surface area of a cube, all you have to do is find the surface area of one side of the cube and then multiply it by six. If you want to know how to find the surface area of a cube, just follow these steps.
Steps
Calculating the Surface Area Knowing the Length of One Side
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1Understand that the surface area of a cube is made up of the areas of its six faces. Since all of the faces of a cube are congruent, we can just find the area of one face and multiply it by 6 to get the total surface area. The surface area can be found by using a simple formula: 6 x s2, where "s" represents a side of the cube.[1]
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2Find the area of one side of the cube. To find the area of one side of the cube, you need to find "s," which represents the side length of a cube, and then find s2. This really means that you'll be multiplying the length of the cube's side times its width to find its area -- the length and width of a cube's side just happen to be the same. If one side of the cube, or "s," is equal to 4 centimeter (1.6 in), then the area of the side of the cube is (4 cm)2, or 16 cm2. Remember to state your answer in square units.[2]Advertisement
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3Multiply the area of the side of the cube by 6. Now that you've found the area of one side of the cube, all you have to do to find the surface area is to multiply this number by 6. 16 cm2 x 6 = 96 cm2. The surface area of the cube is 96 cm2.[3]
Calculating the Surface Area Knowing the Volume
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1Find the volume of the cube. Let's say that the volume of the cube is 125 cm3.[4]
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2Find the cube root of the volume. To find the cube root of the volume, just look for a number that can be cubed to become the volume, or use your calculator. The number won't always be a whole number. In this case, with the number 125 is a perfect cube, and its cube root is 5, because 5 x 5 x 5 = 125. So, "s," or one side of the cube, is 5.[5]
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3Plug this answer into the formula for finding the surface area of a cube. Now that you know the length of one side of a cube, just plug it into the formula for finding the surface area of a cube: 6 x s2. Since the length of one side is 5 centimeter (2.0 in), just plug it into the formula like this: 6 x (5 cm)2.[6]
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4Solve. Just do the math. 6 x (5 cm)2 = 6 x 25 cm2 = 150 centimeter (59.1 in) 2.
Community Q&A
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QuestionWhat if the cube has different lengths -- for example 3 cm, 4 cm and 3 cm?
Community AnswerAll cubes have equal sides. If they aren't equal, they are call rectangular prisms. -
QuestionHow do I find the total surface area of a cube whose volume is 3?
DonaganTop AnswererYou would have to refer to a table that gives cube roots, because the formula for finding the surface area of this cube is six times the cube root of 9. -
QuestionHow do I find the volume of the cube if I only know the surface area?DonaganTop AnswererDivide the surface area by 6. That gives you the area of one side. Find the square root of that area. That gives you the length of one edge. Cube that number. That's the volume (in cubic units).
References
- ↑ https://www.mathopenref.com/cubearea.html
- ↑ https://math.libretexts.org/Bookshelves/Arithmetic_and_Basic_Math/Book%3A_Basic_Math_(Grade_6)/01%3A_Area_and_Surface_Area/06%3A_Squares_and_Cubes/6.02%3A_Surface_Area_of_a_Cube
- ↑ https://www.softschools.com/math/geometry/topics/surface_area_of_a_cube/
- ↑ https://sciencing.com/calculate-surface-area-volume-5171869.html
- ↑ https://www.cuemath.com/measurement/surface-area-of-cube/
- ↑ https://www.cuemath.com/measurement/surface-area-of-cube/
About This Article
To find the surface area of a cube, use the formula: surface area = 6s^2, where s is the length of one of the sides. If you don't know the length of the sides, you can find the surface area using volume. Just find the cube root of the volume, which is equal to the length of one side of the cube. Then, plug that number into the formula for finding the surface area. For examples you can work through, read on!
