How to Calculate the Surface Area of a Cube (By Length or Volume)

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Easy formulas and step-by-step instructions (with example problems)
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The surface area of an object is the combined area of all of the faces on its surface. All 6 faces of a cube are identical, so to find the surface area of a cube, all you have to do is find the surface area of one face of the cube and then multiply it by 6. We chatted with pro math tutor David Jia to explain how to find the surface area of a cube if you know either the length of one side or the volume of the cube, as well as how to understand cubes and surface area better.

Surface Area of a Cube Formula

The formula for finding the surface area of a cube is 6s 2 , or 6 times the surface area of one face of the cube. The surface area of one face equals the length of one face s of the cube squared. Then, multiply this by 6, since a cube has 6 identical faces.

Section 1 of 4:

Calculating Surface Area with the Length of One Side

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  1. This is the equation for the surface area of a cube. S stands for “side,” or the length of one side of a cube. To find the total surface area of a cube, we need to know the area of one of the square faces of the cube first. To find the area of a square, multiplying the length times the width (since the 4 sides of a square are equal, the length and width are the same number).
    • Once we know the area of a single face of the cube, all we need to do is multiply that value by 6, since a cube has 6 faces.
    • So, just find the area of once face of the cube, then multiply that by 6! That’s all this equation really means.
  2. First, we find the area of one face of the cube. Every face of a cube is a square. The area of a square is length times width , and length and width are always the same on a square. So all we need to do is square the measurement we’re given ( s ), which means multiply it times itself. [1]
    • For example, if we’re told that one edge, or side, of a cube is 4 cm, then we find the area of one face of the cube by multiplying 4 cm x 4 cm, which is 16 cm 2 .
    • In other words, s 2 = (4 cm) 2 = 4 cm x 4 cm = 16 cm 2
    • Our units are squared ( 2 ) because we’re also multiplying the unit by itself. Centimeters x centimeters = centimeters 2 .
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  3. Now that you've found the area of one face of the cube, all you have to do to find the surface area is multiply this number by 6, since a cube has 6 identical faces. 16 cm 2 x 6 = 96 cm 2 . The surface area of the cube in this example is 96 cm 2 .
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Section 2 of 4:

Calculating the Surface Area with the Volume

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  1. The volume of a cube is length x width x height . Since it’s a cube, the length, width, and height are all the same value, so really we’re just multiplying one number ( s , or "side") by itself 3 times, or “cubing” it. If we already know the volume of a cube, we can use this information to work backward and find the surface area. [2]
    • For example, let's say that the volume of the cube we’re working with is 125 cm 3 .
  2. To find the cube root of the volume, we’ll need to factor the primes of the volume. To do this, look for a number that can be multiplied by itself 3 times to equal the volume. You may need to use a calculator, and keep in mind that the number won't always be a whole number. Finding the cube root will tell us the length of one side of the cube, which we can use to easily calculate surface area.
    • In this case, the cube root of 125 is 5, since 5 x 5 x 5 = 5 3 = 125. So, s , or the length of one side of our cube, is 5 cm.
  3. 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: 6s 2 . Since the length of one side is 5 cm, just plug it into the formula like this:
    • 6 x (5 cm) 2
    • 6 x (5 cm x 5 cm)
    • 6 x 25 cm 2 = 150 cm 2 .
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Section 3 of 4:

Understanding Cubes & Surface Area

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  1. Take a look at a picture frame on a wall. If we say, “The surface area of the picture frame,” we’re talking about the flat space inside that frame. This space can be measured in square units . [3]
    • For 2-dimensional objects, we typically find surface area by multiplying the length times the width.
    • For 3-dimensional objects like cubes, we find the surface area of all the different faces and add them together for the total surface area.
    • The units are square because area is a two-dimensional measurement. It’s not just how tall or wide the shape is, but how tall and wide the shape is. It’s not just length or width, but both of them together!
  2. If you were to take a cube apart like a cardboard box, you’d find that you have 6 identical squares. After all, Jia reminds us, “since it's a cube, that means every side is the same.” Since every side of a cube is the same, we find the surface area simply by finding the area of one side, then multiplying that by 6.
    • For example, if we know the surface area of one side of a cube is 3 square inches, we can say that the total surface area of the cube is 3 sq in. x 6 = 18 sq in.
    • Remember that surface area is always measured in squared units, no matter what the unit actually is. It might be square feet, square meters, square yards, and so on.
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Section 4 of 4:

Avoiding Common Mistakes

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  1. When finding surface area, many people accidentally multiply side x side x side, but that’s how you get volume, not surface area! It’s an easy mistake to make, so remember: surface area of a cube = side x side x 6.
  2. A cube is unique because all of its surfaces are identical, and so are all of its sides. This makes the equation for a cube’s surface area simple, but also different from other shapes’ equations. Avoid using this equation to find the surface area of a rectangular prism, for example.
    • When in doubt, just find the surface area of each individual face on the shape, then add them all together.
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Community Q&A

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  • Question
    What if the cube has different lengths -- for example 3 cm, 4 cm and 3 cm?
    Community Answer
    All cubes have equal sides. If they aren't equal, they are call rectangular prisms.
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  • Question
    How do I find the total surface area of a cube whose volume is 3?
    Donagan
    Top Answerer
    You 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.
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  • Question
    How do I find the volume of the cube if I only know the surface area?
    Donagan
    Top Answerer
    Divide 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).
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      References

      1. ↑ https://math.libretexts.org/Bookshelves/Arithmetic_and_Basic_Math/Basic_Math_(Grade_6)/01%3A_Area_and_Surface_Area/06%3A_Squares_and_Cubes/6.02%3A_Surface_Area_of_a_Cube
      2. ↑ https://math.libretexts.org/Bookshelves/Arithmetic_and_Basic_Math/Basic_Math_(Grade_6)/01%3A_Area_and_Surface_Area/06%3A_Squares_and_Cubes/6.02%3A_Surface_Area_of_a_Cube
      3. ↑ https://flexbooks.ck12.org/cbook/ck-12-cbse-math-class-9/section/13.6/primary/lesson/surface-area-of-a-cube/

      About This Article

      Article Summary X

      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!

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