To determine the correct expression for the volume of a solid right pyramid with a square base, let's first recall the formula for the volume of such 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 with edge length [tex]\( x \)[/tex] cm, we can calculate the base area:
[tex]\[ \text{base\_area} = x^2 \][/tex]
The height of the pyramid is given as [tex]\( y \)[/tex] cm.
Substituting the base area and height into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
Thus, the expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} x^2 y \, \text{cm}^3 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \, \text{cm}^3} \][/tex]
