The problem states that a cubic stand is made of a material with a density of $375 \, \text{kg/m}^3$ and has a mass of $60 \, \text{kg}$. We need to find the side length of this cubic stand.

1. Problem Description

The problem states that a cubic stand is made of a material with a density of $375 \, \text{kg/m}^3$ and has a mass of $60 \, \text{kg}$. We need to find the side length of this cubic stand.

2. Solution Steps

First, we need to use the formula relating density, mass, and volume:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$

We can rearrange this formula to solve for the volume:

$\text{Volume} = \frac{\text{Mass}}{\text{Density}}$

Plugging in the given values, we have:

$\text{Volume} = \frac{60 \, \text{kg}}{375 \, \text{kg/m}^3} = 0.16 \, \text{m}^3$

Now, since the stand is a cube, the volume is related to the side length $s$ by:

$\text{Volume} = s^3$

So, to find the side length $s$, we take the cube root of the volume:

$s = \sqrt[3]{\text{Volume}}$

$s = \sqrt[3]{0.16 \, \text{m}^3}$

$s \approx 0.54288 \, \text{m}$

We need to round the answer to the nearest hundredth of a meter:

$s \approx 0.54 \, \text{m}$

3. Final Answer

Side length = 0.54 m