/*! 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 24 A house is \(50.0 \mathrm{ft}\) ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A house is \(50.0 \mathrm{ft}\) long and \(26 \mathrm{ft}\) wide and has \(8.0-\mathrm{ft}\) high ceilings. What is the volume of the interior of the house in cubic meters and in cubic centimeters?

Short Answer

Expert verified
The volume of the interior of the house is approximately \(3200 \, \mathrm{m}^3\) or \(3,200,000,000 \, \mathrm{cm}^3\).

Step by step solution

01

Calculation of Volume in Cubic Feet

To calculate the volume of the interior of the house in cubic feet, multiply the length, width and height of the house. So, \(50.0 \, \mathrm{ft} \times 26 \, \mathrm{ft} \times 8.0 \, \mathrm{ft}\) gives the volume in cubic feet.
02

Conversion to Cubic Meters

Next, convert the volume from cubic feet to cubic meters. There are approximately 0.0283168 cubic meters in a cubic foot. So, multiply the volume of the house in cubic feet by 0.0283168 to find the volume in cubic meters.
03

Conversion to Cubic Centimeters

Finally, convert the volume from cubic meters to cubic centimeters. There are 1,000,000 cubic centimeters in a cubic meter. So, multiply the volume of the house in cubic meters by 1,000,000 to find the volume in cubic centimeters.

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.

Cubic Feet to Cubic Meters Conversion
Converting from cubic feet to cubic meters is an essential conversion in measurements, especially when dealing with volume across different systems of units.
If you have a volume given in cubic feet and need to express it in cubic meters, this is how you do it: Use the conversion factor that 1 cubic foot equals approximately 0.0283168 cubic meters. To convert a volume from cubic feet to cubic meters, multiply the given volume by this conversion factor.
For example, if you calculated a volume of 10 cubic feet, the conversion would be:
  • 10 cubic feet × 0.0283168 = 0.283168 cubic meters.
This conversion is highly useful in various applications, especially when dimensional requirements switch depending on context, such as architectural plans or various scientific calculations. Not only does it help in converting the space's volume for physical applications, but it is also fundamental for further conversions into other units such as cubic centimeters.
Cubic Meters to Cubic Centimeters Conversion
Once you have your volume in cubic meters, the next step often is converting this measurement into cubic centimeters. This conversion is simplest because the cubic centimeter is a base unit. The important factor to remember is that there are 1,000,000 cubic centimeters in one cubic meter. This means to convert your volume from cubic meters to cubic centimeters, you multiply by 1,000,000.
For example, if you have a volume of 2 cubic meters:
  • 2 cubic meters × 1,000,000 = 2,000,000 cubic centimeters.
Why is this conversion significant? Cubic centimeters are often more practical for measuring smaller or more precise items. In everyday life, many containers or products use cubic centimeters for volume measurement, such as food packaging or scientific equipment. It's a base metric unit which can simplify calculations in physics and other sciences.
Geometry in Physics
The concept of geometry is deeply embedded in the study of physics, providing a critical foundation for understanding the spatial aspects of physical problems.
Using geometric principles, like volume calculations, is necessary for solving many physics-related questions, such as determining the volume of a space or an object. In the question of calculating the volume of a house, the basic geometric formula for the volume of a rectangular prism applies: The formula is:
  • Volume = length × width × height
This mathematical principle is essential for tasks such as calculating air exchange rates in ventilation or heating systems, assessing material quantities, or even in fundamental physical laws like those of thermodynamics where volume plays a critical role. Moreover, understanding these geometric calculations extends beyond physics into fields such as architecture, engineering, and environmental science, where spatial analysis is critical to decision-making and design.

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

Assume that it takes \(7.00\) minutes to fill a \(30.0\)-gal gasoline tank. (a) Calculate the rate at which the tank is filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in hours, required to fill a \(1.00-\mathrm{m}^{3}\) volume at the same rate. (1 U.S. gal \(=231\) in. \(^{3}\) )

In 2013 , the U.S. national debt was about \(\$ 17\) trillion. (a) If payments were made at the rate of \(\$ 1000\) per second, how many years would it take to pay off the debt, assuming that no interest were charged? (b) A dollar bill is about \(15.5 \mathrm{~cm}\) long. If seventeen trillion dollar bills were laid end to end around the Earth's equator, how many times would they encircle the planet? Take the radius of the Earth at the equator to be \(6378 \mathrm{~km}\). (Note: Before doing any of these calculations, try to guess at the answers. You may be very surprised.)

(a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while, federal law mandated that the maximum highway speed would be \(55 \mathrm{mi} / \mathrm{h}\). Use the conversion factor from part (a) to find the speed in kilometers per hour. (c) The maximum highway speed has been raised to \(65 \mathrm{mi} / \mathrm{h}\) in some places. In kilometers per hour, how much of an increase is this over the \(55-\mathrm{mi} / \mathrm{h}\) limit?

A block of gold has length \(5.62 \mathrm{~cm}\), width \(6.35 \mathrm{~cm}\), and height \(2.78 \mathrm{~cm}\). (a) Calculate the length times the width and round the answer to the appropriate number of significant figures. (b) Now multiply the rounded result of part (a) by the height and again round, obtaining the volume. (c) Repeat the process, first finding the width times the height, rounding it, and then obtaining the volume by multiplying by the length. (d) Explain why the answers don't agree in the third significant figure.

One gallon of paint (volume \(=3.79 \times 10^{-3} \mathrm{~m}^{3}\) ) covers an area of \(25.0 \mathrm{~m}^{2}\). What is the thickness of the fresh paint on the wall?

See all solutions

Recommended explanations on Physics 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.