Question

the figure below is a right rectangular prism. which expression represents the volume of the prism? o $\frac{1}{2}x^{3}$ o $\frac{1}{2}x^{3}$ o $\frac{5}{2}x^{3}$ o $\frac{5}{2}x^{3}$

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism is $V = l\times w\times h$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step2: Identify dimensions

From the figure, the length $l=x$, the width $w = x$, and the height $h=\frac{1}{2}x$.

Step3: Calculate volume

Substitute the values into the formula: $V=x\times x\times\frac{1}{2}x=\frac{1}{2}x^{3}$.

Answer:

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