A solid right pyramid has a square base with an edge length of [tex]$x \, \text{cm}[tex]$[/tex] and a height of [tex]$[/tex]y \, \text{cm}$[/tex].

Which expression represents the volume of the pyramid?

A. [tex]\frac{1}{3} x y \, \text{cm}^3[/tex]
B. [tex]\frac{1}{3} x^2 y \, \text{cm}^3[/tex]
C. [tex]\frac{1}{2} x y^2 \, \text{cm}^3[/tex]
D. [tex]\frac{1}{2} x^2 y \, \text{cm}^3[/tex]



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]