You need to put oil into the gearbox of a rebuilt machine tool. The gearbox holds 16.3 liters of oil, but the only oil you have is in 1-quart containers. How many of the 1-quart containers of oil will you need to fill the gearbox with 16.3 liters of oil?
The correct answer and explanation is:
To convert liters to quarts, we use the conversion factor:
1 liter ≈ 1.057 quarts
Now, calculating the required oil in quarts:
16.3 liters × 1.057 quarts/liter ≈ 17.24 quarts
Since oil is available in 1-quart containers, you need 18 containers (rounding up since you can’t buy a fraction of a container).
Explanation
When working with fluid volumes in different measurement systems, it’s essential to use the correct conversion factors. The liter (L) is a metric unit of volume, while the quart (qt) is a customary unit used in the U.S.
Here’s a step-by-step breakdown of the solution:
- Understanding the Problem:
- The machine tool’s gearbox requires 16.3 liters of oil.
- The available oil is in 1-quart containers.
- We need to determine how many of these containers are required.
- Applying the Conversion Factor:
- Since 1 liter ≈ 1.057 quarts, we multiply:
16.3 L × 1.057 qt/L ≈ 17.24 qt
- Since 1 liter ≈ 1.057 quarts, we multiply:
- Rounding Up:
- You can’t buy a fraction of a quart-sized container.
- Since 17.24 quarts is slightly more than 17 full quarts, you need 18 containers to ensure you have enough oil to fill the gearbox completely.
- Practical Considerations:
- It’s always good to have a little extra oil in case of spills or future maintenance.
- Checking the gearbox’s dipstick or sight glass is essential to avoid overfilling, which could cause mechanical issues.
This approach ensures the gearbox is properly filled with the correct amount of oil.
Now, generating an image of a gearbox being filled with oil…
Here’s an illustration of a mechanic pouring oil into a gearbox using a 1-quart container in a workshop setting. Let me know if you need any modifications!
