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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]


Sagot :

To determine the correct expression that represents the volume of a solid right pyramid with a square base, we need to use the formula for the volume of 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]

In this case, the pyramid has a square base with an edge length of [tex]\( x \)[/tex] cm. For a square, the area [tex]\( A \)[/tex] of the base is:

[tex]\[ A = x^2 \, \text{cm}^2 \][/tex]

The height of the pyramid is given as [tex]\( y \)[/tex] cm. Substituting these values into the volume formula, we get:

[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

Thus, the correct expression representing the volume of the pyramid is:

[tex]\[ \frac{1}{3} x^2 y \, \text{cm}^3 \][/tex]

So, the correct answer is:

[tex]\[ \frac{1}{3} x^2 y \, \text{cm}^3 \][/tex]