To determine whether you should buy the golden cube, let's use the given data to check if the cube is actually made of gold by comparing its density with the known density of gold.

Step 1: Calculate the volume of the cube

The formula for the volume $V$ of a cube is: $V = \text{side length}^3$ Here, each side of the cube is 2 cm, so: $V = 2^3 = 8 \, \text{cm}^3$

Step 2: Calculate the density of the cube

Density $\rho$ is given by the formula: $\rho = \frac{\text{mass}}{\text{volume}}$ The mass of the cube is 40.0 grams, and its volume is 8 cm³ (as calculated above). Therefore, the density of the cube is: $\rho = \frac{40.0 \, \text{g}}{8 \, \text{cm}^3} = 5.0 \, \text{g/cm}^3$

Step 3: Compare with the density of gold

The density of pure gold is 19.3 g/cm³. Since the cube's density is only 5.0 g/cm³, it is significantly less dense than pure gold.

Step 4: Conclusion

Since the density of the cube (5.0 g/cm³) is much lower than the density of gold (19.3 g/cm³), the cube is unlikely to be made of solid gold. It may be gold-plated or made of another material entirely.

Based on this, purchasing the cube for $100 is not recommended if you're expecting it to be solid gold, as its composition does not match that of pure gold.

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Would you like more details on how density affects this analysis, or do you have any questions?

Here are 5 related questions for further exploration:

1. How would the price change if the cube were made of a gold alloy instead?
2. What other materials might have a density close to 5.0 g/cm³?
3. How could you test the composition of the cube without damaging it?
4. What is the typical price difference between gold-plated and solid gold objects?
5. If the cube were hollow, how would that affect the calculation of its density?

Tip: When buying metals or precious objects, always verify the material through density or other physical tests, as appearance alone can be deceptive.