To determine the volume of a solid right pyramid with a square base of edge length [tex]\( s \)[/tex] units and height [tex]\( h \)[/tex] units, we can use the well-known formula for the volume of a pyramid. The formula is:
[tex]\[ V = \frac{1}{3} \times (\text{base area}) \times (\text{height}) \][/tex]
1. Calculate the base area:
- Since the base is a square, the area of the base is given by the square of the edge length [tex]\( s \)[/tex]:
[tex]\[ \text{Base area} = s^2 \][/tex]
2. Substitute the base area and height into the volume formula:
- We substitute [tex]\( s^2 \)[/tex] for the base area and [tex]\( h \)[/tex] for the height:
[tex]\[ V = \frac{1}{3} \times s^2 \times h \][/tex]
3. Simplify the expression:
- The expression already appears in its simplest form:
[tex]\[ V = \frac{1}{3} s^2 h \][/tex]
Given this formula, the expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} s^2 h \text{ units}^3 \][/tex]
Therefore, the correct choice among the options is:
[tex]\[ \frac{1}{3} s^2 h \text{ units}^3 \][/tex]
