we know that
The volume of a pyramid is equal to
[tex] V=\frac{1}{3} (area\ of\ the\ base)*heigth [/tex]
in this problem
[tex] area\ of\ the\ base=n^{2}\ units^{2} \\ heigth=(n-1)\ units [/tex]
Substitute in the formula above
[tex] V=\frac{1}{3} (n^{2})*(n-1) [/tex]
[tex] V=\frac{1}{3} (n^{3}-n^{2} )\ units^{3} [/tex]
therefore
the answer is
The volume of the pyramid is equal to
[tex] V=\frac{1}{3} (n^{3}-n^{2} )\ units^{3} [/tex]
The expression represents the volume of the pyramid is [tex]\rm \dfrac{1}{3} (n^3-n^2)[/tex].
The base of a solid right pyramid is a square with an edge length of n units.
The height of the pyramid is n − 1 unit.
The volume of a pyramid is the measure of the number of units occupied by the pyramid.
The volume of a pyramid is measured by the following formula;
[tex]\rm Volume \ of \ pyramid = \dfrac{1}{3} \times base \times height[/tex]
The base of the pyramid is [tex]\rm n^2[/tex] and height is (n-1).
Substitute all the values in the formula;
[tex]\rm Volume \ of \ pyramid = \dfrac{1}{3} \times base \times height\\\\\rm Volume \ of \ pyramid = \dfrac{1}{3} \times n^2\times (n-1)\\\\\rm Volume \ of \ pyramid = \dfrac{1}{3} \times (n^3-n^2)\\\\\rm Volume \ of \ pyramid = \dfrac{1}{3} (n^3-n^2)[/tex]
Hence, the expression represents the volume of the pyramid is [tex]\rm \dfrac{1}{3} (n^3-n^2)[/tex].
To know more about the Volume of the pyramid click the link given below.
https://brainly.com/question/1260835
