To determine the volume of a solid right pyramid with a square base, we'll follow a step-by-step approach to understand the formulas and calculations involved.
1. Base Area Calculation:
The base of the pyramid is a square with an edge length of [tex]\( s \)[/tex] units. To find the area of a square, we use the formula:
[tex]\[
\text{Base Area} = s^2
\][/tex]
This comes from multiplying the side length of the square by itself.
2. Volume of the Pyramid:
For a pyramid, the volume [tex]\( V \)[/tex] is given by:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
Here, the height [tex]\( h \)[/tex] is the perpendicular distance from the base to the apex of the pyramid.
3. Substitute Values:
We substitute the base area [tex]\( s^2 \)[/tex] and the height [tex]\( h \)[/tex] into the volume formula:
[tex]\[
V = \frac{1}{3} \times s^2 \times h
\][/tex]
Therefore, the expression that represents the volume of the solid right pyramid is:
[tex]\[
\frac{1}{3} s^2 h \text{ units}^3
\][/tex]
Among the given options, the correct expression is:
[tex]\[
\boxed{\frac{1}{3} s^2 h \text{ units}^3}
\][/tex]
