To find the volume of a cube, you use the formula:
Volume=side×side×side=s3\text{Volume}=\text{side}\times \text{side}\times \text{side}=s^3Volume=side×side×side=s3
where sss is the length of one side of the cube. Since all sides of a cube are equal, you simply cube the length of any one side to get the volume. For example, if the side length is 4 units, the volume is 43=644^3=6443=64 cubic units
. Alternatively, if you know the length of the cube's diagonal ddd, you can use the formula:
Volume=3×d39\text{Volume}=\frac{\sqrt{3}\times d^3}{9}Volume=93×d3
This comes from the relationship between the diagonal and the side length, where d=s3d=s\sqrt{3}d=s3
. Summary:
- Using side length sss:
V=s3V=s^3V=s3
- Using diagonal length ddd:
V=3×d39V=\frac{\sqrt{3}\times d^3}{9}V=93×d3
The volume is always expressed in cubic units corresponding to the units used for the side length or diagonal
