To determine the volume of a 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 given by:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Here, the base is a square with side length [tex]\( x \)[/tex] cm, so the area of the base [tex]\( A \)[/tex] is:
[tex]\[ A = x^2 \, \text{cm}^2 \][/tex]
Given the height [tex]\( y \)[/tex] cm of the pyramid, we substitute the base area and the height into the volume formula:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \, \text{cm}^3 \][/tex]
After substituting the values and simplifying, the volume of the pyramid becomes:
[tex]\[ V = \frac{1}{3} x^2 y \, \text{cm}^3 \][/tex]
So, the correct option that represents the volume of a pyramid with a square base of length [tex]\( x \)[/tex] cm and height [tex]\( y \)[/tex] cm is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \, \text{cm}^3} \][/tex]
