To determine the volume of a right pyramid with a square base, we need to use the formula for the volume of a pyramid. The formula is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base area} \times \text{Height} \][/tex]
1. Determine the Base Area:
The base of the pyramid is a square. The area of a square with edge length [tex]\( x \)[/tex] is calculated as:
[tex]\[ \text{Base area} = x^2 \][/tex]
2. Determine the Height:
The height of the pyramid is [tex]\( y \)[/tex] cm.
3. Substitute the Values into the Volume Formula:
Substitute the base area and height into the volume formula:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
Therefore, the expression that represents the volume of the pyramid is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \, \text{cm}^3} \][/tex]
Let's compare this with the provided options:
1. [tex]\(\frac{1}{3} x y \, \text{cm}^3\)[/tex]
2. [tex]\(\frac{1}{3} x^2 \cdot \, \text{cm }^3\)[/tex]
3. [tex]\(\frac{1}{2} x^2 \, \text{cm}^3\)[/tex]
4. [tex]\(\frac{1}{2} x^2 y \, \text{cm}^3\)[/tex]
The correct expression that matches our derived formula is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \, \text{cm}^3} \][/tex]
