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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