Question

a solid right pyramid has a square base with an edge length of s units and a height of h units.
which expression represents the volume of the pyramid?
\\(\frac{1}{4} s^2h\\) units\\(^3\\)
\\(\frac{1}{3} s^2h\\) units\\(^3\\)
\\(s^2h\\) units\\(^3\\)
\\(3s^2h\\) units\\(^3\\)

Explanation:

Step1: Recall Volume of Pyramid Formula

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step2: Calculate Base Area

The base is a square with edge length \( s \), so the area of the base \( B = s\times s=s^{2}\).

Step3: Substitute Base Area into Formula

Substitute \( B = s^{2} \) into the volume formula: \( V=\frac{1}{3}\times s^{2}\times h=\frac{1}{3}s^{2}h \).

Answer:

\(\frac{1}{3}s^{2}h\) units\(^3\) (the option corresponding to this expression)