/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 139 A room measures \(10.0 \mathrm{f... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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?

Short Answer

Expert verified
The room's volume is approximately 28038 liters.

Step by step solution

01

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: \[ V = 10.0 \text{ ft} \times 11.0 \text{ ft} \times 9.0 \text{ ft} = 990.0 \text{ cubic feet} \]
02

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, \[ V = 990.0 \text{ ft}^3 \times 0.0283168 \text{ m}^3 / \text{ft}^3 = 28.03763 \text{ m}^3 \]
03

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: \[ V = 28.03763 \text{ m}^3 \times 1000 \text{ liters/m}^3 = 28037.63 \text{ liters} \]
04

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 \[ V \approx 28038 \text{ liters} \].

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

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.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A 124 -g sample of a pure liquid, liquid \(A\), with a density of \(3.00 \mathrm{~g} / \mathrm{mL}\) is mixed with a \(40.8-\mathrm{mL}\) sample of a pure liquid, liquid \(\mathrm{B}\), with a density of \(2.00 \mathrm{~g} / \mathrm{mL}\). What is the total volume of the mixture? (Assume there is no reaction upon the mixing of \(\mathrm{A}\) and \(\mathrm{B}\), and volumes are additive.)

Zinc metal can be purified by distillation (transforming the liquid metal to vapor, then condensing the vapor back to liquid). The metal boils at normal atmospheric pressure at \(1666^{\circ} \mathrm{F}\). What is this temperature in degrees Celsius? in kelvins?

You have a piece of gold jewelry weighing \(9.35 \mathrm{~g}\). Its volume is \(0.654 \mathrm{~cm}^{3}\). Assume that the metal is an alloy (mixture) of gold and silver, which have densities of \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\) and \(10.5 \mathrm{~g} / \mathrm{cm}^{3}\), respectively. Also assume that there is no change in volume when the pure metals are mixed. Calculate the percentage of gold (by mass) in the alloy. The relative amount of gold in an alloy is measured in karats. Pure gold is 24 karats; an alloy of \(50 \%\) gold is 12 karats. State the proportion of gold in the jewelry in karats.

The land area of Greenland is \(840,000 \mathrm{mi}^{2},\) with only \(132,000 \mathrm{mi}^{2}\) free of perpetual ice. The average thickness of this ice is \(5000 \mathrm{ft}\). Estimate the mass of the ice (assume two significant figures). The density of ice is \(0.917 \mathrm{~g} / \mathrm{cm}^{3} .\)

One year of world production of gold was \(49.6 \times 10^{6}\) troy ounces. One troy ounce equals \(31.10 \mathrm{~g}\). What was the world production of gold in metric tons \(\left(10^{6} \mathrm{~g}\right)\) for that year?

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.