The expression represents the volume of the pyramid is \(\rm \dfrac{1}{3} (n^3-n^2)\).
Given
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.
What is the volume of the pyramids?
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;
\(\rm Volume \ of \ pyramid = \dfrac{1}{3} \times base \times height\)
The base of the pyramid is \(\rm n^2\) and height is (n-1).
Substitute all the values in the formula;
\(\rm Volume \ of \ pyramid = \dfrac{1}{3} \times base \times height\\\\\rm Volume \ of \ pyramid = \dfrac{1}{3} \times n^2\times (n-1)\\\\\rm Volume \ of \ pyramid = \dfrac{1}{3} \times (n^3-n^2)\\\\\rm Volume \ of \ pyramid = \dfrac{1}{3} (n^3-n^2)\)
Hence, the expression represents the volume of the pyramid is \(\rm \dfrac{1}{3} (n^3-n^2)\).
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