Problem 48 - College Physics

Question

The interior storage compartment of a restaurant refrigerator measures \(1.3 \mathrm{~m}\) high, \(1.05 \mathrm{~m}\) wide, and \(67 \mathrm{~cm}\) deep. Determine its volume in cubic feet.

Step-by-Step Solution

Answer

The volume is approximately 32.28 cubic feet.

Step 1: Convert dimensions to consistent units

We are given the dimensions of the refrigerator in meters and centimeters. First, convert the depth from centimeters to meters so all dimensions are in meters. To convert 67 cm to meters, use the conversion factor: 1 m = 100 cm.\[ 67 \text{ cm} = \frac{67}{100} \text{ m} = 0.67 \text{ m} \]

Step 2: Calculate volume in cubic meters

Now that all dimensions are in meters, calculate the volume by multiplying the height, width, and depth of the compartment.Let: - Height = 1.3 m- Width = 1.05 m- Depth = 0.67 mVolume in cubic meters = Height \( \times \) Width \( \times \) Depth.\[\text{Volume} = 1.3 \times 1.05 \times 0.67 \] \[\text{Volume} = 0.91455 \text{ cubic meters} \]

Step 3: Convert cubic meters to cubic feet

To convert the volume from cubic meters to cubic feet, use the conversion factor: 1 cubic meter = 35.3147 cubic feet.\[ \text{Volume in cubic feet} = 0.91455 \times 35.3147 \]\[ \text{Volume in cubic feet} = 32.2796 \]

Step 4: Round the result

Typically, answers are rounded to a reasonable number of decimal places. In this case, round the volume to two decimal places.\[ \text{Volume} \approx 32.28 \text{ cubic feet} \]

Key Concepts

Metric to Imperial Conversion

Converting between metric and imperial units is a crucial skill, especially when dealing with international measurements or specifications. In our exercise, we need to convert a volume measured in cubic meters (a metric unit) to cubic feet (an imperial unit). This flexibility is often needed in different industries and disciplines.

The key to any conversion is using the correct conversion factor. For converting cubic meters to cubic feet, the conversion factor is:

• 1 cubic meter = 35.3147 cubic feet

This means that for every cubic meter, there are approximately 35.3147 cubic feet.

When converting, multiply the volume in cubic meters by this factor to get the equivalent volume in cubic feet. This way, you maintain the accuracy of measurement, crucial in fields like architecture, construction, and shipping that require precise volume specifications.

Cubic Meters

Cubic meters are a metric unit of volume. This unit is common in countries using the metric system and is useful for specifying large volumes. A cubic meter can be visualized as a cube with edges of one meter in length, width, and height.

When calculating the volume of an object in cubic meters, all dimensions should be in meters. This ensures that the resulting volume calculation is accurate and straightforward. For instance, in our exercise:

• Height = 1.3 meters
• Width = 1.05 meters
• Depth = 0.67 meters

The volume is obtained by multiplying these three dimensions:

\[ ext{Volume} = 1.3 imes 1.05 imes 0.67 = 0.91455 ext{ cubic meters}\]This precise approach prevents errors during conversion and helps in maintaining a standard measurement across different systems.

Cubic Feet

Cubic feet are part of the imperial system, commonly used in the United States. One cubic foot equals the volume of a cube with sides of one foot each. It's a standard measurement in many markets, where people often estimate room sizes, appliance capacities, or shipment volumes in cubic feet.

In our example, converting from cubic meters to cubic feet involves multiplying the volume in cubic meters by 35.3147. Here's how the conversion goes:
\[ ext{Volume in cubic feet} = 0.91455 imes 35.3147 = 32.2796 \]Finally, rounding the result to two decimal places gives:

• Volume \( \approx 32.28 \) cubic feet

Rounding ensures the result is manageable and practical while still offering a valuable level of precision. This conversion skill is key when collaborating between countries using different measurement systems.