A solid right pyramid has a square base with an edge length of [tex]$x \, \text{cm}$[/tex] and a height of [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 correct expression for the volume of a solid right pyramid with a square base, let's first recall the formula for the volume of such a pyramid.

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]

Given that the base of the pyramid is a square with edge length [tex]\( x \)[/tex] cm, we can calculate the base area:
[tex]\[ \text{base\_area} = x^2 \][/tex]

The height of the pyramid is given as [tex]\( y \)[/tex] cm.

Substituting the base area and height into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

Thus, the expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} x^2 y \, \text{cm}^3 \][/tex]

Therefore, the correct choice is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \, \text{cm}^3} \][/tex]