To find the volume of a solid right pyramid with a square base, we need to use the formula for the volume of 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]
Given that the base of the pyramid is a square, the area of the base (which we will denote as [tex]\( \text{Base Area} \)[/tex]) can be calculated using the edge length of the square (denoted as [tex]\( x \)[/tex]). The area of a square is given by:
[tex]\[
\text{Base Area} = x^2
\][/tex]
We are also given the height of the pyramid (denoted as [tex]\( y \)[/tex]). Plugging these values into our volume formula, we get:
[tex]\[
V = \frac{1}{3} \times x^2 \times y
\][/tex]
So, the expression that represents the volume of the pyramid is:
[tex]\[
\frac{1}{3} x^2 y \, \text{cm}^3
\][/tex]
Among the given options, this matches with:
[tex]\[
\frac{1}{3} x^2 y \, \text{cm}^3
\][/tex]
Therefore, the correct option is:
[tex]\[
\boxed{\frac{1}{3} x^2 y \, \text{cm}^3}
\][/tex]
