Let's determine the correct expression for the volume of a solid right pyramid that has a square base with an edge length of [tex]\(x\)[/tex] cm and a height of [tex]\(y\)[/tex] cm.
1. Identify the base area of the pyramid:
- The base of the pyramid is square, so to find the area of the square base, we use the formula for the area of a square, which is:
[tex]\[
\text{Area of the base} = x^2 \text{ cm}^2
\][/tex]
2. Recall the formula for the volume of a pyramid:
- The volume [tex]\(V\)[/tex] of a pyramid is given by:
[tex]\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
3. Substitute the values in the formula:
- We already know that the base area is [tex]\(x^2\)[/tex] and the height is [tex]\(y\)[/tex]. Substituting these into the volume formula, we get:
[tex]\[
V = \frac{1}{3} \times x^2 \times y
\][/tex]
4. Simplify and express the volume:
- Simplifying this, the volume of the pyramid becomes:
[tex]\[
V = \frac{1}{3} x^2 y \text{ cm}^3
\][/tex]
Therefore, the correct expression that represents the volume of the pyramid is:
[tex]\[
\frac{1}{3} x^2 y \text{ cm}^3
\][/tex]
The correct choice is:
[tex]\[
\boxed{\frac{1}{3} x^2 y \text{ cm}^3}
\][/tex]
