To find the volume of a solid right pyramid with a square base, we follow these steps:
1. Identify the given parameters:
- The edge length of the square base is [tex]\( x \)[/tex] cm.
- The height of the pyramid from the base to the apex is [tex]\( y \)[/tex] cm.
2. Determine the area of the square base:
- Since the base is a square with edge length [tex]\( x \)[/tex], the area of the base (A) is given by:
[tex]\[
A = x^2 \, \text{cm}^2
\][/tex]
3. Recall the formula for the volume of a pyramid:
- The general formula for the volume (V) of a pyramid is:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
4. Substitute the base area and height into the formula:
- Base Area = [tex]\( x^2 \, \text{cm}^2 \)[/tex]
- Height = [tex]\( y \)[/tex] cm
- Plug these into the volume formula:
[tex]\[
V = \frac{1}{3} \times x^2 \times y \, \text{cm}^3
\][/tex]
5. Match the expression to the given choices:
- The correct 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]
