There are 1.057 quarts in 1 Liter. There are 4 cups in one quart. Your water bottle reads 1500 mL. How many cups is this? (Hint: convert mL to L before you begin dimensional analysis) A. 0.3975 cups B. 2.515 cups C. 6.342 cups
The Correct Answer and Explanation is:
To find out how many cups are in a 1500 mL water bottle, we follow these steps using dimensional analysis:
Step 1: Convert milliliters to liters
We know that:
1000 mL = 1 L
So:
1500 mL ÷ 1000 = 1.5 L
Step 2: Convert liters to quarts
We know that:
1 L = 1.057 quarts
So:
1.5 L × 1.057 quarts/L = 1.5855 quarts
Step 3: Convert quarts to cups
We know that:
1 quart = 4 cups
So:
1.5855 quarts × 4 cups/quart = 6.342 cups
Final Answer:
C. 6.342 cups
Explanation:
The key to solving this problem is using dimensional analysis step by step. The first thing to notice is that the water bottle is measured in milliliters, and the final answer needs to be in cups. Since milliliters and cups are not directly convertible, we bridge the units by first converting milliliters to liters, then liters to quarts, and finally quarts to cups.
In the first step, 1500 mL is equal to 1.5 liters. This is a basic metric conversion and allows us to work with the unit of liters, which is commonly used for volume in scientific contexts.
Next, we convert liters to quarts using the provided ratio of 1.057 quarts per liter. This conversion helps us move from the metric system to the customary U.S. system of volume.
Lastly, since there are four cups in every quart, multiplying the number of quarts by 4 gives the number of cups.
By completing all three conversions carefully and multiplying across each step, we reach the accurate result of 6.342 cups. This step-by-step method ensures precision and helps avoid errors in unit conversion.
