To determine the volume of a solid right pyramid with a square base, we need to follow a few steps:
1. Understand the Volume Formula for a Pyramid:
The general formula for the volume [tex]\( V \)[/tex] of a pyramid is:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
2. Calculate the Base Area:
Since the pyramid has a square base, the area of the square base can be calculated using the edge length [tex]\( s \)[/tex]. The area [tex]\( A \)[/tex] of a square with edge length [tex]\( s \)[/tex] is:
[tex]\[
A = s^2
\][/tex]
3. Substitute the Base Area and Height into the Volume Formula:
The height of the pyramid is given as [tex]\( h \)[/tex]. Using the formula for the volume of a pyramid, we substitute the base area and height:
[tex]\[
V = \frac{1}{3} \times s^2 \times h
\][/tex]
So, the expression that represents the volume of the solid right pyramid with a square base and height [tex]\( h \)[/tex] is:
[tex]\[
\frac{1}{3} s^2 h
\][/tex]
Therefore, the correct choice from the given options is:
[tex]\[
\frac{1}{3} s^2 h \text{ units}^3
\][/tex]
