To find the length of a side of a cube when given its volume, you can use the formula for the volume of a cube:

$V = s^3$

Where:

• $V$ is the volume of the cube.
• $s$ is the length of a side of the cube.

Given: $V = 42875 \, \text{cm}^3$

To find the side length $s$, you take the cube root of the volume:

$s = \sqrt[3]{V}$

Substitute the given volume:

$s = \sqrt[3]{42875 \, \text{cm}^3}$

Now, let's calculate the cube root.

$s \approx 35.01 \, \text{cm}$

So, the length of each side of the cube is approximately 35.01 cm.

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Would you like more details or have any questions? Here are some related questions:

1. How do you find the surface area of the cube using the side length?
2. If the volume of a cube is doubled, what happens to the length of its sides?
3. What is the relationship between the side length and the diagonal of the cube?
4. How would you calculate the volume if you only knew the surface area of the cube?
5. How can the concept of a cube's volume be applied to solve real-world problems?

Tip: When dealing with cubes, remember that all sides are equal, which simplifies calculations compared to other 3D shapes!