To determine the correct expression that represents 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]
In this case, the pyramid has a square base with an edge length of [tex]\( x \)[/tex] cm. For a square, the area [tex]\( A \)[/tex] of the base is:
[tex]\[ A = x^2 \, \text{cm}^2 \][/tex]
The height of the pyramid is given as [tex]\( y \)[/tex] cm. Substituting these values into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
Thus, the correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3} x^2 y \, \text{cm}^3 \][/tex]
So, the correct answer is:
[tex]\[ \frac{1}{3} x^2 y \, \text{cm}^3 \][/tex]
