Thus, because the diagonal of a cube's face and two of the sides on that face form a right triangle, d 2 = s 2 + s 2 = 2 s 2. This is because, according to the Pythagorean theorem, the square of the hypotenuse of a right triangle is equal to the sums of the squares of the other two sides. Note that, in general terms, d 2 = 2 s 2 where d is the length of the diagonal of one of the cube's faces and s is the length of one of the sides of the cube.Now that we know the side length, we can find the volume of the cube by multiplying 4.96 3 = 122.36 feet 3. We would find the side length of the cube by dividing 7/√2 = 4.96 feet. For instance, let's say that one of a cube's faces has a diagonal that is 7 feet long.From here, it's relatively simple to cube your answer and find the volume of the cube as described above. Thus, if the only information you're given about a cube is regarding the diagonal length of one of its faces, you can find the side length for the cube by dividing this value by √2. By definition, the diagonal of a perfect square is √2 × the length of one of its sides. In the next few steps, we'll use this information to find the cube's volume.ĭivide the diagonal across one of the cube's faces by √2 to find the cube's side length. As a running example, let's say that we have a cube whose surface we know to be 50 cm 2, but we don't know its side lengths.We'll use this formula to find the volume of the cube from its surface area. This formula is essentially the same as finding the 2-dimensional area of the cube's six faces and adding these values together. The surface area of a cube is given via the formula 6 s 2, where s is the length of one of the cube's sides.In this section, we'll walk through this process step-by-step. From here, all you'll need to do is cube the length of the side to find the volume as normal. For instance, if you know a cube's surface area, all you need to do to find its volume is to divide the surface area by 6, then take the square root of this value to find the length of the cube's sides. The length of a cube's side or the area of one of its faces can be derived from several other of the cube's properties, which means that if you start with one of these pieces of information, you can find the volume of the cube in a roundabout manner. While the easiest way to find a cube's volume is to cube the length of one of its sides, it's not the only way.
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