To find the side length of the cube formed by 1 kg of gold, we will use the formula for the volume of a cube and the fact that:

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

Given:

• Mass of gold: 1 kg = 1000 grams
• Density of gold: 19.3 g/cm³
• Volume of a cube: $V = s^3$ where $s$ is the side length.

Steps:

1. Use the formula for density: $\text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{1000 \, \text{g}}{19.3 \, \text{g/cm}^3}$ Calculating this: $\text{Volume} \approx 51.81 \, \text{cm}^3$

2. Since $V = s^3$, solve for $s$: [ s = \sqrt[3]{\text{Volume}} = \sqrt[3]{51.81} ]

   Calculating the cube root: $s \approx 3.73 \, \text{cm}$

So, the side length of the cube is approximately 3.73 cm.

Would you like more details or have any questions?

Related questions:

1. What would the side length be if the mass of gold was 2 kg?
2. How does changing the density affect the side length of the cube?
3. What is the volume of a cube with a side length of 4 cm?
4. If the gold is reshaped into a sphere, what would be the radius?
5. How does the volume formula change for different shapes like spheres or cylinders?

Tip: Cube roots can be calculated using scientific calculators or cube root functions in most software packages like Excel or Python.