Problem 139 - General Chemistry

Question

A room measures \(10.0 \mathrm{ft} \times 11.0 \mathrm{ft}\) and is \(9.0 \mathrm{ft}\) high. What is its volume in liters?

Step-by-Step Solution

Answer

The room's volume is approximately 28038 liters.

Step 1: Calculate the Volume in Cubic Feet

First, find the volume of the room in cubic feet by multiplying its length, width, and height. The formula for volume is given by: \[ V = ext{length} imes ext{width} imes ext{height} \] which results in: \[ V = 10.0 \text{ ft} \times 11.0 \text{ ft} \times 9.0 \text{ ft} = 990.0 \text{ cubic feet} \]

Step 2: Convert Cubic Feet to Cubic Meters

To convert the volume from cubic feet to cubic meters, use the conversion factor that 1 cubic foot is approximately 0.0283168 cubic meters. Therefore, \[ V = 990.0 \text{ ft}^3 \times 0.0283168 \text{ m}^3 / \text{ft}^3 = 28.03763 \text{ m}^3 \]

Step 3: Convert Cubic Meters to Liters

Since 1 cubic meter is equal to 1000 liters, multiply the volume in cubic meters by 1000 to find the volume in liters: \[ V = 28.03763 \text{ m}^3 \times 1000 \text{ liters/m}^3 = 28037.63 \text{ liters} \]

Step 4: Round the Volume in Liters (Optional)

For simplicity or practicality, you might round the volume to a desired level of precision. Here, you can round to two decimal places: \[ V \approx 28037.63 \text{ liters} \] or depending on the context, you might prefer \[ V \approx 28038 \text{ liters} \].

Key Concepts

Volume Calculation

Understanding how to calculate the volume of a space is an essential skill in various fields, like architecture and interior design.
The volume of an object or space is essentially how much space it occupies, and it's usually expressed in cubic units.
When calculating the volume of a rectangular room or box, the process involves using the dimensions of the space.
For a room with defined length, width, and height, the formula is straightforward:

• Volume (V) = Length × Width × Height

Using this formula ensures that you're taking into account all three dimensions of the space, all measured in the same unit, which for this example, was feet.

Once you multiply these values, you arrive at a volume in cubic feet, which is perfect for spaces within the U.S. standard measurement system.

Cubic Feet to Cubic Meters Conversion

Often in scientific and international contexts, you need to convert measurements into the metric system for consistency or comparability.
In our example, we are converting from cubic feet, which is an imperial measurement, to cubic meters, a metric measurement.

To make this conversion, you’ll need to use a conversion factor:

• 1 cubic foot is approximately 0.0283168 cubic meters.

Use this factor by multiplying the volume in cubic feet by 0.0283168.
This process transitions your value from cubic feet to cubic meters effectively, which is often more useful for calculations in scientific fields or countries using the metric system.
Converting units like this ensures that everyone can understand and use the data efficiently, no matter where they are located in the world.

Liters Conversion

Once you have your volume in cubic meters, converting this into liters is the next step, especially if it applies to water usage or chemical volumes.
In the metric system, 1 cubic meter is equivalent to 1000 liters. This is a simple and convenient conversion factor to remember:

• Volume in liters (L) = Volume in cubic meters (m³) × 1000

By multiplying your volume in cubic meters by 1000, you'll obtain the volume in liters.
This conversion is extremely helpful, particularly for industries requiring precise liquid measurements, such as cooking, pharmacology, and environmental science.
With these metrics, operations and calculations regarding volume become far more tangible and applied in everyday contexts.