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Chapter 1: Problem 12

Two types of barrel units were in use in the 1920 s in the United States. The apple barrel had a legally set volume of 7056 cubic inches; the cranberry barrel, 5826 cubic inches. If a merchant sells 20 cranberry barrels of goods to a customer who thinks he is receiving apple barrels, what is the discrepancy in the shipment volume in liters?

Short Answer

Expert verified
The discrepancy in the shipment volume is 402.12 liters.

Step by step solution

01

Understand the Barrel Volumes

Identify the volumes of the two barrel types: the apple barrel has a volume of 7056 cubic inches and the cranberry barrel has a volume of 5826 cubic inches.
02

Calculate the Volume Difference Per Barrel

Find the difference in volume between one apple barrel and one cranberry barrel: \[ Volume\text{ difference per barrel} = 7056 \text{ cubic inches} - 5826 \text{ cubic inches} = 1230 \text{ cubic inches} \]
03

Calculate Total Discrepancy for 20 Barrels

Multiply the volume difference per barrel by the number of barrels sold to find the total discrepancy: \[ Total\text{ discrepancy} = 1230 \text{ cubic inches/barrel} \times 20 \text{ barrels} = 24600 \text{ cubic inches} \]
04

Convert Cubic Inches to Liters

Use the conversion factor: 1 cubic inch = 0.0163871 liters.Convert the total discrepancy from cubic inches to liters: \[ 24600 \text{ cubic inches} \times 0.0163871 \text{ liters/cubic inch} = 402.11796 \text{ liters} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

cubic inches to liters conversion
Converting from cubic inches to liters involves a specific formula. Cubic inches and liters are both units of volume, but they belong to different measurement systems 鈥� the imperial and the metric systems, respectively. The conversion factor between these two units is that 1 cubic inch equals roughly 0.0163871 liters. With this factor, you can easily convert any volume given in cubic inches to liters.
For example, to convert 24600 cubic inches to liters, you multiply the number of cubic inches by the conversion factor:
\( 24600 \text{ cubic inches} \times 0.0163871 \text{ liters/cubic inch} = 402.11796 \text{ liters} \).
Understanding this conversion is essential, especially in situations involving different measurement systems.
barrel volume calculation
Calculating the volume of barrels is necessary to determine discrepancies in transactions, especially when different standards exist for barrel sizes. In the given exercise, two types of barrel units are used: the apple barrel (7056 cubic inches) and the cranberry barrel (5826 cubic inches).
The approach to calculate the discrepancy involves a few steps:
  • First, identify the volumes of the barrels involved in cubic inches.
  • Second, find the difference in volume between one apple barrel and one cranberry barrel. This step is done using the formula:
    \( Volume\text{ difference per barrel} = 7056 \text{ cubic inches} - 5826 \text{ cubic inches} = 1230 \text{ cubic inches} \)
  • Third, multiply the volume difference per barrel by the number of barrels sold. This gives the total discrepancy in cubic inches:
    \( Total\text{ discrepancy} = 1230 \text{ cubic inches/barrel} \times 20 \text{ barrels} = 24600 \text{ cubic inches} \)
By following these calculations, you can determine volume discrepancies for any number of barrels.
unit discrepancy
Unit discrepancy can occur when different standards or units are used without proper conversion. This issue arises frequently in trade and commerce, where products may be measured using various units. In the provided exercise, the discrepancy arises because a merchant sells barrels measured in cranberry barrel units while the customer expects them in apple barrel units.
The difference in volume between one apple barrel and one cranberry barrel is 1230 cubic inches. If the merchant sells 20 cranberry barrels, the customer receives less volume than expected by a total of 24600 cubic inches. When converted to liters, this discrepancy is 402.11796 liters.
Addressing unit discrepancies involves proper understanding and conversion of units. Always ensure that both parties in a transaction agree on the units being used to avoid misunderstandings and discrepancies.
Unit discrepancy reminds us of the importance of standardizing measurements globally to facilitate smoother and more accurate transactions.

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Most popular questions from this chapter

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