Questions: In liposuction, a doctor removes fat deposits from a person's body. If body fat has a density of 0.909 g/mL and 3.0 L of fat is removed, how many pounds of fat are removed from the patient? Express your answer using two significant figures.

Solution Steps

To solve this problem, we need to follow these steps:

1. Convert the volume of fat removed from liters to milliliters.
2. Use the density of body fat to find the mass in grams.
3. Convert the mass from grams to kilograms.
4. Convert the mass from kilograms to pounds using the given conversion factor.

To convert the volume of fat removed from liters to milliliters, we use the conversion factor \(1 \, \text{L} = 1000 \, \text{mL}\): \[ \text{Volume in mL} = 3.0 \, \text{L} \times 1000 \, \text{mL/L} = 3000 \, \text{mL} \]

Using the density of body fat, we can calculate the mass in grams: \[ \text{Mass in g} = \text{Volume in mL} \times \text{Density in g/mL} = 3000 \, \text{mL} \times 0.909 \, \text{g/mL} = 2727.0 \, \text{g} \]

To convert the mass from grams to kilograms, we use the conversion factor \(1 \, \text{kg} = 1000 \, \text{g}\): \[ \text{Mass in kg} = \frac{2727.0 \, \text{g}}{1000} = 2.7270 \, \text{kg} \]

Using the conversion factor \(1 \, \text{kg} = 2.20 \, \text{lb}\), we convert the mass to pounds: \[ \text{Mass in lb} = 2.7270 \, \text{kg} \times 2.20 \, \text{lb/kg} = 6.0 \, \text{lb} \]

Final Answer