Gold has a density of 19.3 g/cm^3. What is the mass, in kg of a cube of gold measuring 2.0 inches on each side? Use unit analysis, NOT the density formula.

To solve this using unit analysis, we'll convert all units consistently and proceed step-by-step:

### Given:
- Density of gold: \( 19.3 \, \text{g/cm}^3 \)
- Side length of the cube: \( 2.0 \, \text{inches} \)
- Goal: Find the mass in kilograms (kg)

### Steps:

1. **Convert the side length from inches to centimeters (cm)**:
   - \( 1 \, \text{inch} = 2.54 \, \text{cm} \)
   - \( 2.0 \, \text{inches} \times 2.54 \, \text{cm/inch} = 5.08 \, \text{cm} \)

2. **Calculate the volume of the cube**:
   - The volume \( V \) of a cube is given by \( \text{side}^3 \).
   - \( V = (5.08 \, \text{cm})^3 = 131.79 \, \text{cm}^3 \)

3. **Determine the mass in grams (g)**:
   - The density of gold is \( 19.3 \, \text{g/cm}^3 \), so the mass is:
   \[
   \text{Mass} = \text{density} \times \text{volume}
   \]
   \[
   \text{Mass} = 19.3 \, \text{g/cm}^3 \times 131.79 \, \text{cm}^3 = 2543.55 \, \text{g}
   \]

4. **Convert grams to kilograms**:
   - \( 1 \, \text{kg} = 1000 \, \text{g} \), so:
   \[
   \text{Mass in kg} = \frac{2543.55 \, \text{g}}{1000} = 2.54355 \, \text{kg}
   \]

Thus, the mass of the cube of gold is approximately **2.54 kg**.

Would you like any further details or explanations?

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Here are 5 related questions to expand on this:

1. How does the mass change if the side length of the cube doubles?
2. What would the mass be if the density were 10 g/cm³ instead?
3. How would you calculate the mass if the shape was a sphere instead of a cube?
4. Can you use this method to find the mass of other metals with known densities?
5. What is the weight of the cube in Newtons if measured on Earth?

**Tip:** Always ensure units are consistent when applying unit analysis, as incorrect conversions can lead to significant errors.

Gold has a density of 19.3 g/cm^3. What is the mass, in kg, of a cube of gold measuring 2.0 inches on each side? Use unit analysis, NOT the density formula.

Find the mass of a cube of gold with a density of 19.3 g/cm³ and sides measuring 2.0 inches using unit analysis. This solution involves converting inches to centimeters, calculating the volume of the cube, and determining mass in kilograms. Suitable for high school students learning unit conversion and volume calculation.

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