Question

The world's record for the largest cup of coffee was broken on October 15, 2010, with a 2010-gal cup of coffee in Las Vegas, Nevada. If a cup of coffee contains \(473 \mathrm{~mL}\) of coffee, how many cups of coffee would be required to fill this coffee cup?

Short answer

Approximately 16,082 cups.

Step-by-step solution

- Convert gallons to milliliters

First, convert the volume of the world's largest cup of coffee from gallons to milliliters. Use the conversion factor: 1 gallon = 3,785.41 milliliters. Calculate the volume in milliliters: \[2010 \text{ gallons} \times 3,785.41 \text{ mL/gallon} = 7,605,671.4 \text{ mL}\]

- Determine the number of regular cups of coffee

Next, find out how many standard cups of coffee (473 mL each) fit into the total volume in milliliters. Divide the total volume by the volume of one cup of coffee: \[ \frac{7,605,671.4 \text{ mL}}{473 \text{ mL/cup}} \ \approx 16,081.503 \text{ cups} \]

- Interpret the Result

Since the number of cups must be a whole number, round the result to the nearest whole number: Approximately 16,082 cups of coffee are required to fill the world's largest coffee cup.

Key concepts

Unit Conversion

In chemistry, and in many other scientific fields, unit conversion is crucial for solving problems effectively. It helps to express quantities in different units, making it easier to understand and compare data. For example, if you need to convert gallons to milliliters, you use a conversion factor. A conversion factor is a ratio that expresses how units relate to each other. In our case, 1 gallon is equivalent to 3,785.41 milliliters. This allows us to convert the given volume in gallons to milliliters. So, you simply multiply the number of gallons by the conversion factor:

\[2010 \text{ gallons} \times 3,785.41 \text{ mL/gallon} = 7,605,671.4 \text{ mL}\]

Using conversion factors correctly ensures that your calculations are accurate.

Volume Measurement

Volume measurement can be important in both everyday life and scientific experiments. Volume is the amount of space an object or substance occupies. In this exercise, we deal with both large and small volumes. The world's largest cup of coffee holds 2010 gallons, a much larger unit of volume than a standard coffee cup's 473 milliliters. Understanding how to measure and convert volumes is essential. It allows you to get accurate results when dealing with different sized containers. By converting 2010 gallons to milliliters, we can easily compare it to regular coffee cups. Remember, accurate volume measurement often involves:

• Knowing the units involved (gallons, milliliters, liters, etc.)
• Using the correct tools (measuring cups, graduated cylinders, etc.)
• Applying the appropriate conversion factors

Volume measurement is all about careful observation and taking constant measurements.

Problem-Solving Steps

Approaching a problem systematically can make even complex tasks manageable. Let's break down our coffee cup example into clear steps:

1. **Identify the Given Information**: We know the world's largest coffee cup holds 2010 gallons, and a regular cup holds 473 mL.

2. **Convert Units**: Convert gallons to milliliters using the factor 1 gallon = 3,785.41 mL:

\[2010 \text{ gallons} \times 3,785.41 \text{ mL/gallon} = 7,605,671.4 \text{ mL}\]

3. **Calculate the Desired Quantity**: Determine how many regular cups (473 mL each) fit into the total volume:

\[ \frac{7,605,671.4 \text{ mL}}{473 \text{ mL/cup}} simeq 16,081.503 \text{ cups}\]

4. **Interpret the Result**: Round your result to the nearest whole number since the number of cups must be a whole number. Hence, approximately 16,082 cups of coffee are required.

Following these steps ensures that you address all aspects of a problem methodically and correctly.