Problem 42 - Chemistry The Science in Context

Question

A swimming pool is \(1.12 \mathrm{m}\) decp at one end and 72 in decp at the other. Which is the deeper end?

Step-by-Step Solution

Answer

Answer: The end with a depth of 72 inches is deeper.

Step 1: Conversion of units

First, we will convert 72 inches to meters. To do this, we will use the following conversion factor: 1 inch = 0.0254 meters. Multiply 72 inches by this conversion factor to find the depth of this end in meters. Depth in meters = \(72 inches \times 0.0254 \frac{meters}{inch}\)

Step 2: Calculate the depth in meters

Now, we will calculate the depth in meters for the end given in inches. Depth in meters = \(72 inches \times 0.0254 \frac{meters}{inch} = 1.8288 meters\)

Step 3: Comparing depths

Now that both depths are in meters, we can compare them to determine which end is deeper: Depth at end 1: 1.12 meters Depth at end 2: 1.8288 meters Since 1.8288 meters is greater than 1.12 meters, the second end (72 inches) is deeper.

Key Concepts

Depth Comparison

To determine which end of the swimming pool is deeper, we need to compare the depths at each end. However, these depths are given in different units - meters and inches. Comparing directly would be like comparing apples to oranges: they are not the same. Thus, a common unit of measurement is required for an accurate comparison. This is a crucial step in problems that involve depth comparison or measurements given in different units.

Once the depths are converted to a common unit, such as meters in this case, making the comparison becomes straightforward. The depth that has the larger numerical value indicates the deeper end. If you're given depths in different units, remember to convert them first before comparing. This simple step can prevent potential errors and ensure an accurate understanding of the problem at hand.

Inches to Meters

Converting inches to meters requires understanding the relationship between these two units of measurement. Inches are part of the imperial system, commonly used in the United States, while meters are part of the metric system, which is widely used internationally. The conversion factor between inches and meters is something you should memorize if you often encounter these conversions. Specifically,

• 1 inch is equal to 0.0254 meters.

To convert from inches to meters, you simply multiply the number of inches by this conversion factor. For instance, to convert 72 inches to meters, you calculate:

• Depth in meters = \(72 ext{ inches} imes 0.0254 \frac{ ext{meters} }{ ext{inch} }\)
• = \(1.8288 ext{ meters}\).

This straightforward multiplication allows you to easily switch between these units when necessary.

Measurement Conversion

Measurement conversion is a fundamental concept applied in various fields like science, engineering, and everyday scenarios. It requires using appropriate conversion factors to switch between different units. In our specific example, we dealt with converting inches to meters, a process essential when dealing with international standards or different systems of measurement.

To convert measurements correctly, follow these steps:

• Identify the units you're starting with and the units you need to convert to.
• Find the known conversion factor. For example, from inches to meters, this factor is 0.0254.
• Multiply the original measurement by the conversion factor. This will give you the measurement in the desired unit.

This skill is not only handy for exercises in math or physics but is also practical in everyday tasks like cooking, traveling, or crafting, where different measurement standards might apply.