Answer :
To find the volume of a solid right pyramid with a square base, we need to use the formula for the volume of a pyramid. This formula is:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
In this case, the base of the pyramid is a square with an edge length of [tex]\( x \)[/tex] cm. Therefore, the area of the base (which is a square) is given by:
[tex]\[ \text{Base Area} = x \times x = x^2 \ \text{cm}^2 \][/tex]
The height of the pyramid is [tex]\( y \)[/tex] cm.
Now, substituting the area of the base and the height into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \ \text{cm}^3 \][/tex]
So, the expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} x^2 y \ \text{cm}^3 \][/tex]
Thus, the correct expression from the given options 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]
In this case, the base of the pyramid is a square with an edge length of [tex]\( x \)[/tex] cm. Therefore, the area of the base (which is a square) is given by:
[tex]\[ \text{Base Area} = x \times x = x^2 \ \text{cm}^2 \][/tex]
The height of the pyramid is [tex]\( y \)[/tex] cm.
Now, substituting the area of the base and the height into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \ \text{cm}^3 \][/tex]
So, the expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} x^2 y \ \text{cm}^3 \][/tex]
Thus, the correct expression from the given options is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \ \text{cm}^3} \][/tex]
