To calculate the volume of the alcohol sample, we can use the formula:

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

Rearranging the formula to solve for volume:

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

Given:

• Mass = 1587.57 g
• Density = 6.6 lb/gal

Since the units are mixed (grams for mass and pounds per gallon for density), we need to convert them into consistent units. Let's break it down:

1. Convert the mass from grams to pounds: $1 \, \text{pound} = 453.592 \, \text{grams}$ So, $\text{Mass in pounds} = \frac{1587.57 \, \text{g}}{453.592 \, \text{g/lb}} = 3.5 \, \text{lb}$

2. Now, using the formula for volume: $\text{Volume in gallons} = \frac{3.5 \, \text{lb}}{6.6 \, \text{lb/gal}} = 0.53 \, \text{gallons}$

3. Convert gallons to liters: $1 \, \text{gallon} = 3.78541 \, \text{liters}$ So, $\text{Volume in liters} = 0.53 \, \text{gal} \times 3.78541 \, \text{L/gal} = 2.00 \, \text{L}$

Thus, the volume of the alcohol sample is approximately 2.00 liters.

Would you like any further details or explanations?

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Here are 5 related questions you might explore:

1. How would the volume change if the density were higher?
2. What is the relationship between density and volume if the mass is constant?
3. How does temperature affect the density of alcohol?
4. How would the calculation change if the alcohol were measured in kilograms?
5. What is the significance of using consistent units when calculating volume?

Tip: Always ensure your units are consistent when performing calculations involving physical quantities like mass, volume, and density.