What is the formula to calculate the side length of a cube given its volume in cubic millimeters?
The sides in meters of a cube that has a volume of 588 cubic millimeters can be calculated as follows:
Given:
Volume (V) = 588 cubic millimeters
To find the side length (S) in meters, we can use the formula:
\[S = \sqrt[3]{V}\]
Substitute the volume into the formula:
\[S = \sqrt[3]{588}\]
\[S = 8.378 \, \text{mm}\]
To convert millimeters to meters, we divide by 1000:
\[S = 0.008378 \, \text{m}\]
Therefore, the side length of a cube with a volume of 588 cubic millimeters is approximately 0.008378 meters.
Understanding Cube Volume and Side Length
Volume Calculation:
To calculate the volume of a cube, we use the formula:
\[V = s^3\]
Where:
V = Volume
s = Side length of the cube
In this case, we are given the volume of the cube as 588 cubic millimeters. By taking the cube root of the volume, we can find the side length of the cube.
Conversion to Meters:
Since the volume is given in cubic millimeters and we are required to find the side length in meters, we need to convert millimeters to meters. This can be done by dividing the value in millimeters by 1000.
Practical Example:
Imagine a cube with a volume of 588 cubic millimeters. By calculating the cube root of this volume, we find that the side length of the cube is approximately 0.008378 meters. This means that each side of the cube measures 0.008378 meters.
Significance of Cubic Millimeters:
A cubic millimeter is a unit of volume that represents a cube with each side measuring 1 millimeter. It is commonly used in scientific measurements, especially in situations where small volumes need to be accurately measured. By understanding the relationship between volume and side length, we can determine the dimensions of a cube based on its volume.
By applying the formula and conversion factor, we can easily calculate the side length of a cube given its volume in cubic millimeters. This helps in understanding the spatial dimensions of an object and is useful in various scientific and engineering applications.