To find the volume of a solid right pyramid with a square base and a specific height, we use the formula for the volume of a pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
In this case, the base of the pyramid is a square with an edge length of [tex]\( x \)[/tex] cm. Therefore, the area of the square base ([tex]\(\text{Base Area}\)[/tex]) is calculated as follows:
[tex]\[ \text{Base Area} = x \times x = x^2 \text{ square centimeters} \][/tex]
Given that the height of the pyramid is [tex]\( y \)[/tex] cm, we can substitute the base area and the height into the volume formula:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
Therefore, the expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} x^2 y \text{ cubic centimeters} \][/tex]
Thus, the correct choice from the given options is:
[tex]\[ \frac{1}{3} x^2 y \; \text{cm}^3 \][/tex]
So, the answer is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \; \text{cm}^3} \][/tex]
