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 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]