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The density formula is a fundamental concept in physics and chemistry that connects mass and volume. The formula is given by: \[ \text{mass} = \text{density} \times \text{volume} \] In this equation:

• Mass is the amount of matter in the object, typically measured in grams (\text{g}).
• Density is the mass per unit volume of a substance, expressed in grams per milliliter (\text{g/mL}).
• Volume is the space that the object occupies, commonly measured in milliliters (\text{mL}) or liters (\text{L}).

The formula reveals that if you know the density and volume of a material, you can easily calculate its mass. For instance, if you have a liquid with a density of 1.4 \text{g/mL} and a volume of 150 \text{mL}, you just multiply these values to get the mass. Simple, right? This fundamental relationship is a powerful tool and is widely used in various scientific calculations.

Calculating mass using the density formula involves straightforward arithmetic. Let's take a closer look at how it's done: \[ \text{mass} = \text{density} \times \text{volume} \]

Part (a): Given that the density of a liquid is 1.4 \text{g/mL}, and its volume is 150 \text{mL}, we find the mass as follows:
\[ \text{mass}_{\text{(a)}} = 1.4 \text{g/mL} \times 150 \text{mL} = 210 \text{g} \]

Part (b): For a glucose solution with a density of 1.15 \text{g/mL} and a volume of 0.500 \text{L}, first convert the volume to milliliters:
\[ 0.500 \text{L} = 500 \text{mL} \] Then calculate the mass:
\[ \text{mass}_{\text{(b)}} = 1.15 \text{g/mL} \times 500 \text{mL} = 575 \text{g} \]

Part (c): To find the mass of a bronze figure with a density of 7.8 \text{g/mL} and a volume of 225 \text{mL}:
\[ \text{mass}_{\text{(c)}} = 7.8 \text{g/mL} \times 225 \text{mL} = 1755 \text{g} \] This step-by-step process simplifies mass calculation using given density and volume values.

Unit conversion is often necessary in mass calculations to ensure all units are compatible. Here's a closer look at converting units:

• Volume Conversion: Sometimes, volume is given in liters (L) but needs to be in milliliters (mL) for mass calculation. Remember, 1 L = 1000 mL. For example, 0.500 L is converted to 500 mL.
• Mass Conversion: Calculated mass might need to be in different units. Commonly, conversions between grams (g) and ounces (oz) are required. The conversion factor is: \[ 1 \text{gram} = 0.035274 \text{ounces} \] Using this factor, you can easily convert grams to ounces. For example, if the mass is 1755 g, it converts to ounces as follows: \[ \text{mass}_{\text{(c)}, \text{oz}} = 1755 \text{g} \times 0.035274 \text{oz/g} = 61.92 \text{oz} \]

Unit conversion ensures the calculated mass matches the desired units, simplifying the use of data in real-world applications.