To find the volume of a solid right pyramid with a square base, we need to follow a few steps and apply the appropriate formula.
1. Understand the given parameters:
- The edge length of the square base is [tex]\( x \)[/tex] cm.
- The height of the pyramid is [tex]\( y \)[/tex] cm.
2. Determine the area of the base:
- The base of the pyramid is a square with edge length [tex]\( x \)[/tex].
- The area of a square is calculated as the side length squared.
[tex]\[
\text{Base area} = x^2 \, \text{cm}^2
\][/tex]
3. Recall the volume formula for 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]
4. Substitute the known values into the formula:
- We already calculated the base area as [tex]\( x^2 \)[/tex].
- The height of the pyramid is given as [tex]\( y \)[/tex].
- Plug these into the volume formula:
[tex]\[
V = \frac{1}{3} \times x^2 \times y
\][/tex]
5. Final expression:
- The volume of the pyramid is:
[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]\[
\boxed{\frac{1}{3} x^2 y \, \text{cm}^3}
\][/tex]
