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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 find the volume of a solid right pyramid with a square base and a specific height, we use the formula for the volume of a pyramid:

[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 square base ([tex]\(\text{Base Area}\)[/tex]) is calculated as follows:

[tex]\[ \text{Base Area} = x \times x = x^2 \text{ square centimeters} \][/tex]

Given that the height of the pyramid is [tex]\( y \)[/tex] cm, we can substitute the base area and the 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]\[ \frac{1}{3} x^2 y \text{ cubic centimeters} \][/tex]

Thus, the correct choice from the given options is:

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

So, the answer is:

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