What is the surface area of a 4x4x4 cube?

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V = volume

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Enter any 1 known variable for a cube into this online calculator to calculate 4 other unknown variables. A cube is a special case where l = w = h for a rectangular prism.

Units: Note that units are shown for convenience but do not affect the calculations.  The units are in place to give an indication of the order of the results such as ft, ft2 or ft3.  For example, if you are starting with a in mm, your calculations will result with V in mm3, S in mm2 and d in mm.

Formulas for a cube:

• Volume of a cube:
• Surface area of a cube:
  • the area of each face (a x a) times 6 faces
  • S = 6a2
• Face diagonal of a cube:
  • By the pythagorean theorem we know that
  • f2 = a2 + a2
  • Then f2 = 2a2
  • solving for f we get
  • f = a√2
• Diagonal of the solid cube:
  • Again, by the pythagorean theorem we know that
  • d2 = a2 + f2
  • substituting f into this equation we get
  • d2 = a2 + (a√2)2 = a2 + 2a2 = 3a2
  • solving for d we get
  • d = a√3

A cube is a special case of a rectangular prism where l = w = h.

For more information on cuboids see: Weisstein, Eric W. "Cuboid." From MathWorld--A Wolfram Web Resource, 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.

1. 1

   Understand 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] X Research source Go to source

2. 2

   Find 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] X Research source Go to source

3. 3

   Multiply 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] X Research source Go to source

1. 1

   Find the volume of the cube. Let's say that the volume of the cube is 125 cm3.[4] X Research source Go to source

2. 2

   Find 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] X Research source Go to source

3. 3

   Plug 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.

4. 4

   Solve. Just do the math. 6 x (5 cm)2 = 6 x 25 cm2 = 150 centimeter (59.1 in) 2.

• Question

  What if the cube has different lengths -- for example 3 cm, 4 cm and 3 cm?

  All cubes have equal sides. If they aren't equal, they are call rectangular prisms.

• Question

  How do I find the total surface area of a cube whose volume is 3?

  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.

• Question

  How do I find the volume of the cube if I only know the surface area?

  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).

wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. To create this article, 30 people, some anonymous, worked to edit and improve it over time. This article has been viewed 405,611 times.

Co-authors: 30

Updated: June 1, 2022

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Categories: Calculating Volume and Area

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