To determine which expression represents the volume of a right pyramid with a square base, let's go through the formula for the volume of the pyramid step by step:
1. Identify the base area:
- The base of the pyramid is a square.
- If the edge length of the square base is [tex]\( x \)[/tex] cm, then the area of the square base ([tex]\( A \)[/tex]) is:
[tex]\[
A = x^2 \text{ cm}^2
\][/tex]
2. Identify the height:
- The height of the pyramid ([tex]\( h \)[/tex]) from the base to the apex is given as [tex]\( y \)[/tex] cm.
3. Volume formula:
- 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]
4. Substitute the base area and height into the formula:
- Using the base area [tex]\( x^2 \)[/tex] and the height [tex]\( y \)[/tex], we have:
[tex]\[
V = \frac{1}{3} \times x^2 \times y \text{ cm}^3
\][/tex]
Thus, the correct expression that represents the volume of the pyramid is:
[tex]\[
\frac{1}{3} x^2 y \text{ cm}^3
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\frac{1}{3} x^2 y \text{ cm}^3}
\][/tex]
