How to Find the Surface Area of a Cube

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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.

Method 1
Method 1 of 2:

Calculating the Surface Area Knowing the Length of One Side

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    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 s 2 , where "s" represents a side of the cube. [1]
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    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 s 2 . 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 cm 2 . Remember to state your answer in square units. [2]
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    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 cm 2 x 6 = 96 cm 2 . The surface area of the cube is 96 cm 2 . [3]
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Method 2
Method 2 of 2:

Calculating the Surface Area Knowing the Volume

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    Let's say that the volume of the cube is 125 cm 3 . [4]
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    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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    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 s 2 . 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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    Just do the math. 6 x (5 cm) 2 = 6 x 25 cm 2 = 150 centimeter (59.1 in) 2 .
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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://www.mathopenref.com/cubearea.html
      2. ↑ 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
      3. ↑ https://www.softschools.com/math/geometry/topics/surface_area_of_a_cube/
      4. ↑ https://sciencing.com/calculate-surface-area-volume-5171869.html
      5. ↑ https://www.cuemath.com/measurement/surface-area-of-cube/
      6. ↑ https://www.cuemath.com/measurement/surface-area-of-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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