StudySmarter - The all-in-one study app.

4.8 • +11k Ratings

More than 3 Million Downloads

Free

StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

How much space does a pen or an elephant take up? How much space do you take up? The volume of an object is something we might often refer to, but what is a volume exactly, how do we measure volumes, and what units do we use to describe a volume?Although the volume of something is a very intuitive notion,…

Content verified by subject matter experts

Free StudySmarter App with over 20 million students

Explore our app and discover over 50 million learning materials for free.

Volume

- Astrophysics
- Absolute Magnitude
- Astronomical Objects
- Astronomical Telescopes
- Black Body Radiation
- Classification by Luminosity
- Classification of Stars
- Cosmology
- Doppler Effect
- Exoplanet Detection
- Hertzsprung-Russell Diagrams
- Hubble's Law
- Large Diameter Telescopes
- Quasars
- Radio Telescopes
- Reflecting Telescopes
- Stellar Spectral Classes
- Telescopes
- Atoms and Radioactivity
- Fission and Fusion
- Medical Tracers
- Nuclear Reactors
- Radiotherapy
- Random Nature of Radioactive Decay
- Thickness Monitoring
- Circular Motion and Gravitation
- Applications of Circular Motion
- Centripetal and Centrifugal Force
- Circular Motion and Free-Body Diagrams
- Fundamental Forces
- Gravitational and Electric Forces
- Gravity on Different Planets
- Inertial and Gravitational Mass
- Vector Fields
- Conservation of Energy and Momentum
- Dynamics
- Application of Newton's Second Law
- Buoyancy
- Drag Force
- Dynamic Systems
- Free Body Diagrams
- Normal Force
- Springs Physics
- Superposition of Forces
- Tension
- Electric Charge Field and Potential
- Charge Distribution
- Charged Particle in Uniform Electric Field
- Conservation of Charge
- Electric Field Between Two Parallel Plates
- Electric Field Lines
- Electric Field of Multiple Point Charges
- Electric Force
- Electric Potential Due to Dipole
- Electric Potential due to a Point Charge
- Electrical Systems
- Equipotential Lines
- Electricity
- Ammeter
- Attraction and Repulsion
- Basics of Electricity
- Batteries
- Capacitors in Series and Parallel
- Circuit Schematic
- Circuit Symbols
- Circuits
- Current Density
- Current-Voltage Characteristics
- DC Circuit
- Electric Current
- Electric Generators
- Electric Motor
- Electrical Power
- Electricity Generation
- Emf and Internal Resistance
- Kirchhoff's Junction Rule
- Kirchhoff's Loop Rule
- National Grid Physics
- Ohm's Law
- Potential Difference
- Power Rating
- RC Circuit
- Resistance
- Resistance and Resistivity
- Resistivity
- Resistors in Series and Parallel
- Series and Parallel Circuits
- Simple Circuit
- Static Electricity
- Superconductivity
- Time Constant of RC Circuit
- Transformer
- Voltage Divider
- Voltmeter
- Electricity and Magnetism
- Benjamin Franklin's Kite Experiment
- Changing Magnetic Field
- Circuit Analysis
- Diamagnetic Levitation
- Electric Dipole
- Electric Field Energy
- Magnets
- Oersted's Experiment
- Voltage
- Electromagnetism
- Electrostatics
- Energy Physics
- Big Energy Issues
- Conservative and Non Conservative Forces
- Efficiency in Physics
- Elastic Potential Energy
- Electrical Energy
- Energy and the Environment
- Forms of Energy
- Geothermal Energy
- Gravitational Potential Energy
- Heat Engines
- Heat Transfer Efficiency
- Kinetic Energy
- Mechanical Power
- Potential Energy
- Potential Energy and Energy Conservation
- Pulling Force
- Renewable Energy Sources
- Wind Energy
- Work Energy Principle
- Engineering Physics
- Angular Momentum
- Angular Work and Power
- Engine Cycles
- First Law of Thermodynamics
- Moment of Inertia
- Non-Flow Processes
- PV Diagrams
- Reversed Heat Engines
- Rotational Kinetic Energy
- Second Law and Engines
- Thermodynamics and Engines
- Torque and Angular Acceleration
- Famous Physicists
- Fields in Physics
- Alternating Currents
- Capacitance
- Capacitor Charge
- Capacitor Discharge
- Coulomb's Law
- Electric Field Strength
- Electric Fields
- Electric Potential
- Electromagnetic Induction
- Energy Stored by a Capacitor
- Equipotential Surface
- Escape Velocity
- Gravitational Field Strength
- Gravitational Fields
- Gravitational Potential
- Magnetic Fields
- Magnetic Flux Density
- Magnetic Flux and Magnetic Flux Linkage
- Moving Charges in a Magnetic Field
- Newton’s Laws
- Operation of a Transformer
- Parallel Plate Capacitor
- Planetary Orbits
- Synchronous Orbits
- Fluids
- Absolute Pressure and Gauge Pressure
- Application of Bernoulli's Equation
- Archimedes' Principle
- Conservation of Energy in Fluids
- Fluid Flow
- Fluid Systems
- Force and Pressure
- Force
- Conservation of Momentum
- Contact Forces
- Elastic Forces
- Force and Motion
- Gravity
- Impact Forces
- Moment Physics
- Moments Levers and Gears
- Moments and Equilibrium
- Pressure
- Resultant Force
- Safety First
- Time Speed and Distance
- Velocity and Acceleration
- Work Done
- Fundamentals of Physics
- Further Mechanics and Thermal Physics
- Bottle Rocket
- Charles law
- Circular Motion
- Diesel Cycle
- Gas Laws
- Heat Transfer
- Heat Transfer Experiments
- Ideal Gas Model
- Ideal Gases
- Kinetic Theory of Gases
- Models of Gas Behaviour
- Newton's Law of Cooling
- Periodic Motion
- Rankine Cycle
- Resonance
- Simple Harmonic Motion
- Simple Harmonic Motion Energy
- Temperature
- Thermal Equilibrium
- Thermal Expansion
- Thermal Physics
- Volume
- Work in Thermodynamics
- Geometrical and Physical Optics
- Kinematics Physics
- Air Resistance
- Angular Kinematic Equations
- Average Velocity and Acceleration
- Displacement, Time and Average Velocity
- Frame of Reference
- Free Falling Object
- Kinematic Equations
- Motion in One Dimension
- Motion in Two Dimensions
- Rotational Motion
- Uniformly Accelerated Motion
- Linear Momentum
- Magnetism
- Ampere force
- Earth's Magnetic Field
- Fleming's Left Hand Rule
- Induced Potential
- Magnetic Forces and Fields
- Motor Effect
- Particles in Magnetic Fields
- Permanent and Induced Magnetism
- Magnetism and Electromagnetic Induction
- Eddy Current
- Faraday's Law
- Induced Currents
- Inductance
- LC Circuit
- Lenz's Law
- Magnetic Field of a Current-Carrying Wire
- Magnetic Flux
- Magnetic Materials
- Monopole vs Dipole
- RL Circuit
- Measurements
- Mechanics and Materials
- Acceleration Due to Gravity
- Bouncing Ball Example
- Bulk Properties of Solids
- Centre of Mass
- Collisions and Momentum Conservation
- Conservation of Energy
- Density
- Elastic Collisions
- Force Energy
- Friction
- Graphs of Motion
- Linear Motion
- Materials
- Materials Energy
- Moments
- Momentum
- Power and Efficiency
- Projectile Motion
- Scalar and Vector
- Terminal Velocity
- Vector Problems
- Work and Energy
- Young's Modulus
- Medical Physics
- Absorption of X-Rays
- CT Scanners
- Defects of Vision
- Defects of Vision and Their Correction
- Diagnostic X-Rays
- Effective Half Life
- Electrocardiography
- Fibre Optics and Endoscopy
- Gamma Camera
- Hearing Defects
- High Energy X-Rays
- Lenses
- Magnetic Resonance Imaging
- Noise Sensitivity
- Non Ionising Imaging
- Physics of Vision
- Physics of the Ear
- Physics of the Eye
- Radioactive Implants
- Radionuclide Imaging Techniques
- Radionuclide Imaging and Therapy
- Structure of the Ear
- Ultrasound Imaging
- X-Ray Image Processing
- X-Ray Imaging
- Modern Physics
- Bohr Model of the Atom
- Disintegration Energy
- Franck Hertz Experiment
- Mass Energy Equivalence
- Nuclear Reaction
- Nucleus Structure
- Quantization of Energy
- Spectral Lines
- The Discovery of the Atom
- Wave Function
- Nuclear Physics
- Alpha Beta and Gamma Radiation
- Binding Energy
- Half Life
- Induced Fission
- Mass and Energy
- Nuclear Instability
- Nuclear Radius
- Radioactive Decay
- Radioactivity
- Rutherford Scattering
- Safety of Nuclear Reactors
- Oscillations
- Energy Time Graph
- Energy in Simple Harmonic Motion
- Hooke's Law
- Kinetic Energy in Simple Harmonic Motion
- Mechanical Energy in Simple Harmonic Motion
- Pendulum
- Period of Pendulum
- Period, Frequency and Amplitude
- Phase Angle
- Physical Pendulum
- Restoring Force
- Simple Pendulum
- Spring-Block Oscillator
- Torsional Pendulum
- Velocity
- Particle Model of Matter
- Physical Quantities and Units
- Converting Units
- Physical Quantities
- SI Prefixes
- Standard Form Physics
- Units Physics
- Use of SI Units
- Physics of Motion
- Acceleration
- Angular Acceleration
- Angular Displacement
- Angular Velocity
- Centrifugal Force
- Centripetal Force
- Displacement
- Equilibrium
- Forces of Nature Physics
- Galileo's Leaning Tower of Pisa Experiment
- Inclined Plane
- Inertia
- Mass in Physics
- Speed Physics
- Static Equilibrium
- Radiation
- Antiparticles
- Antiquark
- Atomic Model
- Classification of Particles
- Collisions of Electrons with Atoms
- Conservation Laws
- Electromagnetic Radiation and Quantum Phenomena
- Isotopes
- Neutron Number
- Particles
- Photons
- Protons
- Quark Physics
- Specific Charge
- The Photoelectric Effect
- Wave-Particle Duality
- Rotational Dynamics
- Angular Impulse
- Angular Kinematics
- Angular Motion and Linear Motion
- Connecting Linear and Rotational Motion
- Orbital Trajectory
- Rotational Equilibrium
- Rotational Inertia
- Satellite Orbits
- Third Law of Kepler
- Scientific Method Physics
- Data Collection
- Data Representation
- Drawing Conclusions
- Equations in Physics
- Uncertainties and Evaluations
- Space Physics
- Thermodynamics
- Heat Radiation
- Thermal Conductivity
- Thermal Efficiency
- Thermodynamic Diagram
- Thermodynamic Force
- Thermodynamic and Kinetic Control
- Torque and Rotational Motion
- Centripetal Acceleration and Centripetal Force
- Conservation of Angular Momentum
- Force and Torque
- Muscle Torque
- Newton's Second Law in Angular Form
- Simple Machines
- Unbalanced Torque
- Translational Dynamics
- Centripetal Force and Velocity
- Critical Speed
- Free Fall and Terminal Velocity
- Gravitational Acceleration
- Kinetic Friction
- Object in Equilibrium
- Orbital Period
- Resistive Force
- Spring Force
- Static Friction
- Turning Points in Physics
- Cathode Rays
- Discovery of the Electron
- Einstein's Theory of Special Relativity
- Electromagnetic Waves
- Electron Microscopes
- Electron Specific Charge
- Length Contraction
- Michelson-Morley Experiment
- Millikan's Experiment
- Newton's and Huygens' Theories of Light
- Photoelectricity
- Relativistic Mass and Energy
- Special Relativity
- Thermionic Electron Emission
- Time Dilation
- Wave Particle Duality of Light
- Waves Physics
- Acoustics
- Applications of Ultrasound
- Applications of Waves
- Diffraction
- Diffraction Gratings
- Doppler Effect in Light
- Earthquake Shock Waves
- Echolocation
- Image Formation by Lenses
- Interference
- Light
- Longitudinal Wave
- Longitudinal and Transverse Waves
- Mirror
- Oscilloscope
- Phase Difference
- Polarisation
- Progressive Waves
- Properties of Waves
- Ray Diagrams
- Ray Tracing Mirrors
- Reflection
- Refraction
- Refraction at a Plane Surface
- Resonance in Sound Waves
- Seismic Waves
- Snell's law
- Spectral Colour
- Standing Waves
- Stationary Waves
- Total Internal Reflection in Optical Fibre
- Transverse Wave
- Ultrasound
- Wave Characteristics
- Wave Speed
- Waves in Communication
- X-rays
- Work Energy and Power
- Conservative Forces and Potential Energy
- Dissipative Force
- Energy Dissipation
- Energy in Pendulum
- Force and Potential Energy
- Force vs. Position Graph
- Orbiting Objects
- Potential Energy Graphs and Motion
- Spring Potential Energy
- Total Mechanical Energy
- Translational Kinetic Energy
- Work Energy Theorem
- Work and Kinetic Energy

Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenHow much space does a pen or an elephant take up? How much space do you take up? The volume of an object is something we might often refer to, but what is a volume exactly, how do we measure volumes, and what units do we use to describe a volume?

Although the volume of something is a very intuitive notion, it can be hard to describe exactly what a volume is. The following is a possible description of volume.

The **volume** of an object is a measure of the amount of 3-dimensional space it takes up.

This means that the volume of an elephant is larger than the volume of a mosquito.

A way of thinking about volume is asking how many sugar cubes would fit inside an object if it were hollow. If object \(1\) would hypothetically contain \(200\) sugar cubes and object \(2\) would contain \(400\), then object \(2\) has a volume that is twice that of object \(1\).

Another (non-countable but more precise) way of thinking about volume is how much water would fit inside an object if it were hollow. If you fill two objects with water and object \(1\) is twice as heavy as object \(2\), then object \(1\) has twice as much volume as object \(2\).

Just like mass, charge, and form, volume is a physical property of an object.

There is no general formula for the volume of objects (if we don’t want to use calculus), but let’s look at a very basic object: a rectangular cuboid. This is the 3-dimensional version of a rectangle, see the figure below.

It has sides of length \(a\), \(b\), and \(c\). If we double \(a\), then twice as many sugar cubes will fit inside the cuboid as before because we basically have two copies of the original cuboid on top of each other. This means that the volume of the cuboid doubles if we double the length \(a\). The same goes for the lengths \(b\) and \(c\). These lengths are the only factors affecting the volume of the rectangular cuboid because they contain all the information necessary to define this object. So, the volume \(V_{\text{r.c.}}\) of the rectangular cuboid must be a constant times the product of the length of all the sides, \(abc\). It happens that the constant is \(1\) so our formula becomes:

\[V_{\text{r.c.}}=abc\]

The volume of all other objects can now be defined via this cuboid: we make an object of which we want to know the volume. We make the object hollow and we fill it up with water. We then pour this water into a tank with a rectangular base such that the water takes the shape of a rectangular cuboid. We measure the three sides of the cuboid the water created and we multiply them to get the volume of our object.

The volume \(V_{\text{cube}}\) of a cube with sides of length \(a\) is the length of one side cubed, so \(V_{\text{cube}}=a^3\) because a cube is just a rectangular cuboid with \(a=b=c\).

We can also use water to actually measure the volume of objects in practice. We start with a completely full rectangular-cuboidal tank of water and dip our object in the water. Some of the water will overflow in this process because the water has to make room for the object to be inside the tank. This amount of room is the volume of the object. If we now remove the object from the water again, the water level in the tank will drop because we removed the volume of our object from the tank. The non-filled part of the tank now has the same volume as the object because we just took the object out of the tank! This non-filled part of the tank will have the form of a rectangular cuboid, so this volume is easy to measure, according to the formula we gave earlier. Voilà, this measured volume is the volume of our object. See the illustration below for a schematic presentation of this process.

What are the dimensions of volume? Let’s take a look at the formula of the volume of our rectangular cuboid. We multiply three distances (from the 3 dimensions in the 3-dimensional space mentioned in the definition of volume) with each other to get a volume, so the dimensions of the volume of a rectangular cuboid must be \(\text{distance}^3\). This automatically means that the dimensions of all volumes must be \(\text{distance}^3\). The standard unit to measure a distance is the meter, so the standard unit to measure a volume is \(\mathrm{m}^3\), or a **cubic meter**.

Another unit of volume that is often used is the liter. It has the symbol \(\mathrm{L}\) and is defined as \(1\,\mathrm{L}=1\,\mathrm{dm}^3=10^{-3}\,\mathrm{m}^3\).

A cube with sides of \(a=2\) has a volume of \(8\,\mathrm{m}^3\) because \(V=a^3=(2\,\mathrm{m})^3=8\,\mathrm{m}^3\). This is \(8000\,\mathrm{L}\).

There are shapes for which the volume is reasonably easily calculated, i.e. without needing any advanced mathematics such as calculus every time you encounter such a shape.

Pyramids have a base and a height perpendicular to this base, see the figure below for an illustration. If the base of the pyramid has an area \(A\) and the pyramid has a height \(h\), then the volume \(V\) of the pyramid is always given by \(V=Ah/3\).

The volume of a ball with radius \(r\) is \(V=\dfrac{4}{3}\pi r^3\).

Note how the dimensions of volume in both of the examples above work out to be \(\text{distance}^3\).

If you ever calculate a volume and notice that it doesn’t have the right dimensions of \(\text{distance}^3\), you have done something wrong. A volume always has dimensions of \(\text{distance}^3\).

The volume of objects is important in a lot of physics questions.

Knowledge of the volume of a gas (for example, a gas held in a closed container) is essential for making conclusions about its density, pressure, and temperature. If we compress a gas to a smaller volume, its pressure will increase: it will push back on us.

Try squeezing a closed water bottle. You won’t get very far, because the decrease in volume of the air in the bottle will cause an increase in pressure, pushing back against you. This decrease in volume is essential for the force pushing back to increase.

When taking a bath, you have to take into account the volume of your body. Because your body takes the place of the water in the bathtub, the bathtub will overflow if your volume is larger than the volume of the non-filled part of the bathtub. Subconsciously, you take into account your own volume when filling up a bathtub.

The volume of an object is a measure of the amount of 3-dimensional space it takes up.

One way of thinking about volume is how much water would fit inside an object if it were hollow.

The volume \(V\) of a rectangular cuboid with sides \(a \), \(b\), and \(c\) is given by \(V=abc\).

We can use a tank of water to measure the volume of objects.

The standard unit of volume is the cubic meter (\(\mathrm{m}^3\)). A liter (\(\mathrm{L}\)) is \(\dfrac{1}{1000}\) of a cubic meter.

A volume always has dimensions of \(\text{distance}^3\).

The volume of a gas is often important when looking at gases in a physics context.

The volume of your own body is important to take into account if you want to take a bath and you don’t want your bathtub to overflow.

*h* and disk radius *r* has a volume of *V=**πr ^{2}h*.

More about Volume

How would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

94% of StudySmarter users achieve better grades.

Sign up for free!94% of StudySmarter users achieve better grades.

Sign up for free!How would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

Free physics cheat sheet!

Everything you need to know on . A perfect summary so you can easily remember everything.

Be perfectly prepared on time with an individual plan.

Test your knowledge with gamified quizzes.

Create and find flashcards in record time.

Create beautiful notes faster than ever before.

Have all your study materials in one place.

Upload unlimited documents and save them online.

Identify your study strength and weaknesses.

Set individual study goals and earn points reaching them.

Stop procrastinating with our study reminders.

Earn points, unlock badges and level up while studying.

Create flashcards in notes completely automatically.

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.