Volume¶
Volume is the amount of space a given object consumes. Volume is measured in a unit to the power of 3. For example \(cm^3\).
Equation¶
For prisms, the general formula: \(base\;area * height\) will establish the volume of the object. However for more complex shapes, more complex formulas will be needed to establish the volume.
Calculate the volume of a cube¶
The general formula will work for cubes, however given that the all lengths are the same in a cube, you can simply do: \(side\;length ^ 3\).
A cube, with a side length of 5cm. What is its volume?
\[
\begin{align}
volume\;of\;a\;cube & = side\;length^3 \\
& = 5^3 \\
& = 125cm^3 \\
\end{align}
\]
Calculate the volume of a cylinder¶
The general formula will work for cylinder, as they are a prism. There is no simplification as there is for cubes. Simply use \(\pi * r^2 * height\).
A cylinder, with a height of 6cm, and a base radius of 3cm. What it its volume?
\[
\begin{align}
volume\;of\;a\;cylinder & = \pi * r^2 * height \\
& = \pi * 9 * 6 \\
& = 54\pi cm^3
\end{align}
\]
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