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A cube is a three-dimensional cube of equal width, height, and length. A cube has six square faces, all of which have equal and perpendicular sides. Calculating the volume of a cube is simple – usually, you just need to calculate the length × width × height of the cube. Since the sides of a cube are all the same length, another way of the volume formula is s ^{3} , where s is the side length of the cube. See the detailed explanation of this calculation in Step 1 below.
Steps
Find the third power of one side of a cube
- To better understand the process of calculating the volume of a cube, follow the process step by step through the following example. Assume the side of the cube is 2 cm . We will use this data to find the volume of the cube in the next step.
- The process is essentially the same as finding the area of the base, and then multiplying it by the cube’s height (or, in other words, length × width × height), since the base area is found by multiplying length with bottom width. Since the length, width, and height of the cube are of equal length, we can shorten this process by the third power of the lengths of any of these sides.
- Let’s continue with the example above. Since the side length of the cube is 2 cm, we can find the volume by multiplying 2 x 2 x 2 (or 2 ^{3} ) = 8 .
- In our example, since the initial unit of measure was cm, the final answer would have to be in “cubic centimeters” (or cm ^{3} ). So our answer 8 will become 8 cm ^{3} .
- If we use a different unit of measure at first, the final volume unit will also be different. For example, if our cube has a side of 2 meters , instead of 2 cm, we will write the unit as cubic meters (m ^{3} ).
Find the volume from the total area
- The total area of the cube is calculated by the formula 6 s ^{2} , where s is the length of the side of the cube. This formula is essentially similar to the formula for calculating the two-dimensional area of each face 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, let’s say we have a cube with a total area of 50 cm ^{2} , but we don’t know the side lengths of the cube. In the next steps, we will use this data to find the volume of the cube.
- In our example, we have the division 50/6 = 8.33 cm ^{2} . Don’t forget the answer to the area of a two-dimensional figure in square units (cm ^{2} , in ^{2} , and the like).
- In our example, √8.33 = 2.89 cm .
- In our example, 2.89 × 2.89 × 2.89 = 24.14 cm ^{3} . Don’t forget to write your answer in blocks.
Find the volume from the diagonal
- For example, suppose one face of a cube has a diagonal length of 2.13 meters . We will find the side length 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} = 3.442951 m ^{3} .
- Note that, according to the general formula, d ^{2} = 2 s ^{2} where d is the length of the diagonal of a cube face 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. Therefore, since the diagonal of a cube face and the two square sides of that face make a right triangle, d ^{2} = s ^{2} + s ^{2} = 2 s ^{2} .
- This formula is derived from the Pythagorean Theorem. D , d , and s form a right triangle with D being the hypotenuse, so we have D ^{2} = d ^{2} + s ^{2} . As calculated above, d ^{2} = 2 s ^{2} , we have D ^{2} = 2 s ^{2} + s ^{2} = 3 s ^{2} .
- For example, suppose we know that the length of the diagonal from one corner on the base of the cube to its opposite corner on the “top” of the cube is 10 m. If we wanted to calculate the volume, we would substitute the value 10 for “D” in the above formula as follows:
- D ^{2} = 3 s ^{2} .
- 10 ^{2} = 3 s ^{2} .
- 100 = 3 s ^{2}
- 33.33 = s ^{2}
- 5.77 m = s. From here, all we need to do to find the volume of the cube is the cubic power of the sides of the cube.
- 5.77 ^{3} = 192.45 m ^{3}
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 67 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 245,573 times.
A cube is a three-dimensional cube of equal width, height, and length. A cube has six square faces, all of which have equal and perpendicular sides. Calculating the volume of a cube is simple – usually, you just need to calculate the length × width × height of the cube. Since the sides of a cube are all the same length, another way of the volume formula is s ^{3} , where s is the side length of the cube. See the detailed explanation of this calculation in Step 1 below.
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