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Module 9: Geometry

Volume

Volume is exclusively a 3D property that defines the amount of space taken up by an object (or the capacity it can hold). 2D shapes are flat, and thus do not have a capacity. This is also calculated using the side lengths but in a different manner. Some examples are provided in the table below.

In this table, V {"version":"1.1","math":"V"} = volume, l {"version":"1.1","math":"l"} = length, w {"version":"1.1","math":"w"} = width, h {"version":"1.1","math":"h"} = height.

Shape Shortcuts and Equations
Cube V = l 3 {"version":"1.1","math":"V=l^3"}
Retangular Prism V = l w h {"version":"1.1","math":"V=lwh"}
Cylinder

(with 2 sets of identical sides)

 V = 2 π r h {"version":"1.1","math":"V=2\pi rh"}

Where h {"version":"1.1","math":"h"} = height of cylinder
Sphere V = 4 3 π r 3 {"version":"1.1","math":"V=\dfrac{4}{3}\pi r^3"}

Where r {"version":"1.1","math":"r"} is the radius of the sphere.
Pyramid with Square Base V = l w h 3 {"version":"1.1","math":"V=\dfrac{lwh}{3}"}

Where h {"version":"1.1","math":"h"} = height of the pyramid from the base to the tip.

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