Question

a solid right pyramid has a square base with an edge length of x cm and a height of y cm. which expression represents the volume of the pyramid? (\frac{1}{3}xy\text{ cm}^3) (\frac{1}{3}x^{2}y\text{ cm}^3) (\frac{1}{2}xy^{2}\text{ cm}^3) (\frac{1}{2}x^{2}y\text{ cm}^3)

Explanation:

Step1: Recall volume formula

The volume formula for a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height.

Step2: Calculate base - area

Since the base is a square with edge - length $x$, the area of the base $B = x\times x=x^{2}$.

Step3: Substitute values

The height of the pyramid is $y$. Substituting $B = x^{2}$ and $h = y$ into the volume formula $V=\frac{1}{3}Bh$, we get $V=\frac{1}{3}x^{2}y$.

Answer:

$\frac{1}{3}x^{2}y\ cm^{3}$