Answer :
To determine the volume of a solid right pyramid with a square base, we can use the following formula for the volume \( V \) of a pyramid:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Given that the base of the pyramid is a square with edge length \( x \) cm, the area of the base (\( \text{Base Area} \)) can be calculated by squaring the edge length:
[tex]\[ \text{Base Area} = x^2 \, \text{cm}^2 \][/tex]
The height of the pyramid is given as \( y \) cm.
Now, substituting the base area and the height into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
This simplifies to:
[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]
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
Given that the base of the pyramid is a square with edge length \( x \) cm, the area of the base (\( \text{Base Area} \)) can be calculated by squaring the edge length:
[tex]\[ \text{Base Area} = x^2 \, \text{cm}^2 \][/tex]
The height of the pyramid is given as \( y \) cm.
Now, substituting the base area and the height into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
This simplifies to:
[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]
