Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The definition of length (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. In ancient times, volume is measured using similar-shaped natural containers and later on, standardized containers. Some simple three-dimensional shapes can have its volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Zero-, one- and two-dimensional objects have no volume; in fourth and higher dimensions, an analogous concept to the normal volume is the hypervolume. (Wikipedia).
This video introduces volume and shows how to determine the volume of a cube and rectangular solid. http://mathispower4u.com
From playlist Volume and Surface Area (Geometry)
This video provides a basic introduction to volume.
From playlist Volume and Surface Area (Geometry)
Volume and Capacity (Converting between units of volume)
More resources available at www.misterwootube.com
From playlist Applications of Measurement
Chapter 5 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 2 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 1 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 4 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
Chapter 6 of the Dimensions series. See http://www.dimensions-math.org for more information. Press the 'CC' button for subtitles.
From playlist Dimensions
From playlist h. Three-Dimensional Measurement
A. Song - On the essential minimal volume of Einstein 4-manifolds (version temporaire)
Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
A. Song - On the essential minimal volume of Einstein 4-manifolds
Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Lizhi Chen - Topological complexity of manifolds via systolic geometry
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Lizhi Chen, Lanzhou University Title: Topological complexity of manifolds via systolic geometry Abstract: We discuss homology and homotopy complexity of manifolds in terms of Gromov’s systolic inequality. The optimal const
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
What does a triple integral represent?
► My Multiple Integrals course: https://www.kristakingmath.com/multiple-integrals-course Skip to section: 0:15 // Recap of what the double integral represents 1:22 // The triple integral has two uses (volume and mass) 1:45 // How to use the triple integral to find volume 8:59 // Why the
From playlist Calculus III
A. Song - What is the (essential) minimal volume? 1 (version temporaire)
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
A. Song - What is the (essential) minimal volume? 1
I will discuss the notion of minimal volume and some of its variants. The minimal volume of a manifold is defined as the infimum of the volume over all metrics with sectional curvature between -1 and 1. Such an invariant is closely related to "collapsing theory", a far reaching set of resu
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Gauss's Divergence theorem is one of the most powerful tools in all of mathematical physics. It is the primary building block of how we derive conservation laws from physics and translate them into partial differential equations. @eigensteve on Twitter eigensteve.com databookuw.com %%
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
ME564 Lecture 23: Gauss's Divergence Theorem
ME564 Lecture 23 Engineering Mathematics at the University of Washington Gauss's Divergence Theorem Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L23.pdf Course Website: http://faculty.washington.edu/sbrunton/me564/ http://faculty.washington.edu/sbrunton/
From playlist Engineering Mathematics (UW ME564 and ME565)
Visualization of the Divergence and Curl of a vector field. My Patreon Page: https://www.patreon.com/EugeneK
From playlist Physics
Determine the Volume of a Cube (Decimals)
This video explains how to determine the volume of a rectangular cube. http://mathispower4u.com
From playlist Volume and Surface Area (Geometry)
Dilution Problems, Chemistry, Molarity & Concentration Examples, Formula & Equations
This chemistry video tutorial explains how to solve common dilution problems using a simple formula using concentration or molarity with volume. This video also provides the equations needed to calculate the concentration of a solution after evaporation and after mixing two solutions with
From playlist New AP & General Chemistry Video Playlist