Content

• Steps

A cube is a three-dimensional shape of equal width, height and length. A cube has six square faces, all of which have sides equal and perpendicular to each other. Calculating the volume of a cube is very simple - usually, you just have to length × width × height of the cube. Since the sides of the cube are all equal lengths, another way of the volume formula is S, Inside S is the length of the side of the cube. Please see a detailed explanation of this calculation in Step 1 below.

Steps

Method 1 of 3: Find the one-sided cubic power of the cube

1. 

   Find the length of one side of the cube. Usually, when a problem requires you to find the volume of a cube, you will know the length of one side of the cube. Once you have this number, you are ready to find the volume of the cube. If you are not solving a theoretical problem but trying to find the volume of an actual object with the shape of the cube, use a ruler or a tape measure to measure the side of the cube.
   • To better understand the process of calculating the volume of a cube, follow each step of the process through the following example. Suppose the edge of the cube is 2 cm. We will use this data to find the volume of the cube in the next step.

2. 

   
   
   Tertiary powers of side length. Once you've found the side lengths of the cube, power up the cubic. In other words, multiply this number by itself twice. If S is the side length you will calculate S × S × S (or, more simply, S). This formula will give the volume value of the cube!
   • The process is essentially the same as finding the area of ​​the base, then multiplying by the height of the cube (or, in other words, length × width × height), since the base area is found by multiplying length to base width. Since the length, width, and height of a cube are of equal length, we can shorten this process by making a cubic power of the lengths of any of these sides.
   • Let's continue with the above example. Since the side length of a cube is 2 cm, we can find volume by multiplying 2 x 2 x 2 (or 2) = 8.

3. 

   
   
   Mark your answers with a bae symbol. Since volume is a measure of three-dimensional space, the rule is that your answer should be in the cubic form. Normally, in school math exercises, if you do not pay attention to write your answers in the correct units, you will lose points, so don't forget to use the correct units!
   • In our example, since the original unit of measure was cm, the final answer will be in "cubic centimeters" (or cm). Thus, our answer 8 becomes 8 cm.
   • If we were to use a different unit of measure at first, the final unit of volume will also be different. For example, if our cube has an edge of 2 metersInstead of 2 cm, we will write the unit as cubic meters (m).
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Method 2 of 3: Find the volume from the total area

1. 

   
   
   Find the total area of ​​the cube. Way easiest To find the volume of a cube is its one-sided cubic power, but that's not the way only. The length of one side of a cube or the area of ​​a side of a cube can be deduced from other properties of the cube, that is, if you start with one of these data, you can Find the volume of the cube using the slightly longer one. For example, if you know the total area of ​​a cube, all you need to do is Divide the total area of ​​the cube by 6, then square the square root of this value to find the side lengths of the cube.. From there, you just need to power the square of the side lengths to find the volume as usual. In this section, we will perform the calculation step by step.
   • The total area of ​​the cube is calculated using the formula 6S, with S is the length of the side of the cube. This formula is essentially the same as the formula for calculating the two-dimensional area of ​​each side of a hexagon and adding these values ​​together. We will use this formula to calculate the volume of a cube from its total area.
   • For example, suppose we have a cube whose area is all 50 cmBut we don't know the side lengths of the cube yet. In the next steps, we will use this data to find the volume of the cube.

2. 

   Divide the total area of ​​the cube by 6. Since a cube has 6 faces with equal areas, dividing the total area of ​​the cube by 6 will give you the area of ​​one face. This area is equal to the product of the sides of a cube (length × width, width × height, or height × length).
   • In our example, we have the division 50/6 = 8.33 cm. Don't forget that the solution is for the area of ​​a two-dimensional shape square (cm, in, and similar).

3. 

   Calculate the square root of this value. Because the area of ​​one side of the cube is equal S (S × S), the square root of this value will give you the side length of the cube. Once you have the side lengths of a cube, you should have enough data to calculate the volume of the cube as usual.
   • In our example, √8,33 = 2.89 cm.

4. 

   Power this value to find the volume of the cube. Now that you have the side length of the cube, multiply this value (multiply this value by itself twice) to find the volume of the cube as explained in detail above. . Congratulations! You have found the volume of a cube based on its total area.
   • In our example, 2.89 × 2.89 × 2.89 = 24.14 cm. Don't forget to write your answer in block units.
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Method 3 of 3: Find volume from diagonal

1. 

   Divide the diagonal of a cube by √2 to find the side lengths of the cube. In principle, the diagonal of a square is equal to √2 × the length of one side of the square. So, if the only information you have is about the diagonal of a cube, you can find the side length of the cube by dividing the resulting value by √2. From then on, calculating the cubic power of the side lengths and finding the volume of the cube described above is relatively simple.
   • For example, suppose one face of a cube whose diagonal length is 2.13 meters. We'll find the side lengths of the cube by dividing 2.13 / √2 = 1.51 meters. Now that we know the side lengths, we can find the volume of the cube by multiplying 1.51 = 3.442951 m.
   • Note that, according to the general formula, d = 2S with d is the length of the diagonal of a cube and S is the length of the side of the cube. This is because, according to the Pythagorean theorem, the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So, since the diagonal of a cube face and the two square sides of that face create a right triangle, d = S + S = 2S.

2. 

   Square the diagonal from two opposite points on the cube, then divide it by 3 and calculate the square root of the value found to find the side lengths of the cube. If the only data you have about the cube is the diagonal in three-dimensional space drawn from this corner of the cube to the angle with respect to it, you can still find the volume of the cube. Because d becomes a right angle of the right triangle with the hypotenuse being the diagonal between the two corners of the cube we have D = 3S, where D = diagonal in three dimensions connecting the two opposite corners of the cube.
   • This formula is derived from the Pythagorean Theorem. D, d, and S forms a right triangle with D the hypotenuse, so we have D = d + S. As calculated above, d = 2S, We have D = 2S + S = 3S.
   • For example, suppose we know that the length of the diagonal from one corner of the bottom of the cube to its opposite angle on the cube's "top surface" is 10 m. If we wanted to calculate the volume, we would substitute 10 for "D" in the above formula like this:
     • D = 3S.
     • 10 = 3S.
     • 100 = 3S
     • 33,33 = S
     • 5.77 m = s. From here, all we need to do to find the volume of the cube is the side-quadratic power of the cube.
     • 5,77 = 192.45 m
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