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Concept Version 6
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Volume

Volume is a measure of the three-dimensional space an object occupies, usually taken in terms of length, width and height.

Learning Objective

  • Explain how is volume measured geometrically


Key Points

    • Volume is often quantified numerically using an SI derived unit, the cubic meter. However, for liquids the unit of volume used is known as the liter (equivalent to 0.001 cubic meters).
    • This can also be understood as the amount of fluid a submerged object displaces.
    • Volume can be measured for geometrically regular objects by simple formulas. However, more complicated objects are easier to measure with fluid displacement.

Terms

  • cross section

    A section formed by a plane cutting through an object, usually at right angles to an axis.

  • dimension

    A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.


Full Text

Volume is the quantity of three-dimensional space contained by a closed boundary; it is the space that a substance (solid, liquid, gas or plasma) or shape occupies or contains. Volume is often quantified numerically using an SI derived unit, the cubic meter. However, for liquids the unit of volume used is known as the liter (equivalent to 0.001 cubic meters).

Volume is measured geometrically by multiplying an object's three dimensions—usually taken as length, width and height. Some common volumes are taken as follows:

  • The volume of a cube: length times width times height.
  • The volume of a cylinder: the cross-sectional area times the height of the cylinder.
  • The volume of a sphere: 4/3 times the radius cubed times pi.

The volume of a solid can be determined by the volume of liquid it displaces when submerged.

The volume of a container is generally understood as the capacity of the container, meaning the amount of fluid (gas or liquid) the container can hold, rather than the amount of space the container itself displaces. Measuring cups, as seen in , work by taking a known cross sectional area of a cup and multiplying that by a variable height. Since liquid will always cover the cross section (if there is enough liquid), adding more liquid will increase the height inside the container.

Measuring Volume

A measuring cup can be used to measure volumes of liquids. This cup measures volume in units of cups, fluid ounces and millilitres.

Liquids take the shape of their container, filling up the minimum height needed. Gases, on the other hand, take up the maximum amount of volume possible. Thus a measuring cup can accurately measure the volume of a liquid, whereas a gas will always fill the entire container, more or less uniformly, no matter how little gas there is.

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