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Chapter 6: Problem 17

A trunk of a car has a listed luggage capacity of \(18 \mathrm{ft}\) Express the capacity in in \(^{3}, \mathrm{~m}^{3}\), and \(\mathrm{cm}^{3} .\) Show the cor version steps.

Short Answer

Expert verified
The luggage capacity of the car is \(31032 in^{3}\), \(0.509 m^{3}\), or \(509702.4 cm^{3}\)

Step by step solution

01

Convert Cubic Feet to Cubic Inches

There are \(1728\) cubic inches (\(in^3\)) in a cubic foot (\(ft^3\)). Therefore, the volume in cubic inches is obtained by multiplying the given volume (18 \(ft^3\)) by \(1728\). Which results in \(31032 in^{3}\).
02

Convert Cubic Feet to Cubic Meters

There are roughly \(0.0283168\) cubics meters (\(m^3\)) in a cubic foot (\(ft^3\)). Therefore, the volume in cubic meters is obtained by multiplying the original volume (18 \(ft^3\)) by \(0.0283168\). Which results in roughly \(0.509 m^{3}\).
03

Convert Cubic Feet to Cubic Centimeters

Knowing that in \(1 ft^{3}\) there are roughly \(28316.8 cm^{3}\), you multiply the initial volume (18 \(ft^{3}\)) by \(28316.8\). Which results in roughly \(509702.4 cm^{3}\).

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Key Concepts

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

cubic feet to cubic inches
Converting cubic feet to cubic inches is a straightforward process once you know the conversion factor. Remember, each cubic foot contains 1728 cubic inches. This stems from the fact that
  • 1 foot equals 12 inches
  • A cubic foot is obtained by multiplying the length, width, and height (all in feet)
Thus, \[1 \text{ ft}^3 = 12 \times 12 \times 12 = 1728 \text{ in}^3\]
To convert a volume from cubic feet to cubic inches, simply multiply the cubic feet by 1728. For instance, if you have 18 cubic feet: \[18 \times 1728 = 31032 \text{ in}^3\]This shows just how much smaller an inch is compared to a foot when considering volume.
cubic feet to cubic meters
When converting from cubic feet to cubic meters, the process involves understanding the metric system's measurement. One cubic foot is approximately 0.0283168 cubic meters. The conversion process involves multiplying the volume in cubic feet by this conversion factor.
For instance, to convert 18 cubic feet into cubic meters:\[18 \times 0.0283168 = 0.509 \text{ m}^3\]It's important to note that this answer is rounded to three decimal places to make the numbers easier to handle.
  • 1 cubic foot 鈮� 0.0283168 cubic meters
  • You always multiply the cubic feet by 0.0283168 for this conversion
This conversion can help understand the broader, more internationally used metric system.
cubic feet to cubic centimeters
The conversion from cubic feet to cubic centimeters offers insight into the vast difference between the imperial and metric systems, particularly as the cubic centimeter is a much smaller unit than a cubic inch or cubic meter. Approximately 1 cubic foot equals 28316.8 cubic centimeters.
To perform this conversion, multiply the volume in cubic feet by 28316.8.For example:\[18 \times 28316.8 = 509702.4 \text{ cm}^3\]Here, the larger number in cubic centimeters reflects how this unit captures much finer detail. This conversion is particularly useful in scientific fields, where precise measurements are crucial.
  • Understanding: 1 cubic foot 鈮� 28316.8 cubic centimeters
  • Multiply cubic feet by 28316.8 to switch to cubic centimeters
This helps bridge understanding across different measurement systems.

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Most popular questions from this chapter

For Problem \(6.49, b_{\text {Loss }}\) is expressed in feet, \(L\) and \(D\) in inches, \(V\) in ( \(\mathrm{ft} / \mathrm{s}\) ), and \(g\) in (ft/s \(^{2}\) ). What is the appropriate unit for the friction factor \(f\) ?

The value of viscosity of a fluid represents a measure of how easily the given fluid can flow. The higher the viscosity value is, the more resistance the fluid offers to flow. For example, it would require less energy to transport water in a pipe than it would to transport motor oil or glycerin. The viscosity of many fluids is governed by Newton's law of viscosity \(\tau=\mu \frac{d u}{d y}\), where \(\tau\) is shear stress \(\left(\mathrm{N} / \mathrm{m}^{2}\right), \mu\) is viscosity, and \(d u\) is change in flow speed \((\mathrm{m} / \mathrm{s})\) over a height \(d y(\mathrm{~m})\). What is the appropriate unit for viscosity?

In an annealing process-a process wherein materials such as glass and metal are heated to high temperatures and then cooled slowly to toughen them - the following equation may be used to determine the temperature of a thin piece of material after some time \(t\). $$ \frac{T-T_{\text {eavironment }}}{T_{\text {initial }}-T_{\text {environment }}}=\exp \left(-\frac{2 b}{\rho c L} t\right) $$ where $$ \begin{aligned} T &=\text { temperature }\left({ }^{\circ} \mathrm{C}\right) \\ b &=\text { heat transfer coefficient } \\ \rho &=\text { density }\left(\mathrm{kg} / \mathrm{m}^{3}\right) \end{aligned} $$ Those of you who will pursue aerospace, chemical, mechanical, or materials engineering will learn about the underlying concepts that lead to the solution in your heat-transfer class. What is the appropriate unit for h if the preceding equation is to be homogeneous in units? Show all steps of your work.

On a summer day in Phoenix, Arizona, the inside room temperature is maintained at \(68^{\circ} \mathrm{F}\) while the outdoor air temperature is a sizzling \(110^{\circ} \mathrm{F}\). What is the outdoor-indoor temperature difference in: (a) degrees Fahrenheit, (b) degrees Rankine, (c) degrees Celsius, and (d) Kelvin? Is one degree temperature difference in Celsius equal to one temperature difference in Kelvin, and is one degree temperature difference in Fahrenheit equal to one degree temperature difference in Rankine? If so, why?

The angle of twist for a shaft subjected to twistin torque can be expressed by the following equation: $$ \phi=\frac{T L}{J G} $$ where \(\phi=\) the angle of twist in radians \(T=\) applied torque \((\mathrm{N} \cdot \mathrm{m})\) \(L=\) length of the shaft in meter (m) \(J=\) shaft's polar moment of inertia (measure of resistance to twisting) \(G=\) shear modulus of the material \(\left(\mathrm{N} / \mathrm{m}^{2}\right)\) What is the appropriate unit for \(J\), if the equation is to be homogeneous in units?
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