Assume the density of Karo syrup is 1.37 g/mL. What is the volume, in cups, of 2.75 lbs of Karo syrup?
The correct answer and explanation is :
To determine the volume of 2.75 lbs of Karo syrup in cups, we need to convert the weight from pounds to grams and then use the density of Karo syrup to find the volume. Finally, we convert the volume from milliliters (mL) to cups.
Step 1: Convert Pounds to Grams
Since 1 pound (lb) is equivalent to 453.592 grams (g), we first convert the weight of Karo syrup from pounds to grams:
[
2.75 \, \text{lbs} \times 453.592 \, \frac{\text{g}}{\text{lb}} = 1247.38 \, \text{g}
]
Step 2: Use the Density of Karo Syrup to Find Volume
Density is defined as mass per unit volume. The formula for density is:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Rearranging this formula to solve for volume:
[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
]
We are given that the density of Karo syrup is 1.37 g/mL. Now we can use the mass (1247.38 g) and the density to calculate the volume:
[
\text{Volume} = \frac{1247.38 \, \text{g}}{1.37 \, \frac{\text{g}}{\text{mL}}} = 910.64 \, \text{mL}
]
Step 3: Convert Milliliters to Cups
Next, we need to convert the volume from milliliters (mL) to cups. The conversion factor is:
[
1 \, \text{cup} = 240 \, \text{mL}
]
Thus, to find the volume in cups:
[
\text{Volume in cups} = \frac{910.64 \, \text{mL}}{240 \, \text{mL/cup}} = 3.80 \, \text{cups}
]
Final Answer:
The volume of 2.75 lbs of Karo syrup is approximately 3.80 cups.
Explanation:
This calculation involves converting units from pounds to grams and using the given density of Karo syrup to determine the volume. The density helps us understand how much space the mass occupies, and by using the conversion factor for volume from milliliters to cups, we can express the result in a more familiar unit. Thus, 2.75 lbs of Karo syrup is roughly 3.80 cups, considering its density of 1.37 g/mL.