Question

an oblique prism with a square base of edge length x units has a volume of $\frac{1}{2}x^{3}$ cubic units. which expression represents the height of the prism?
$x$ units
$\frac{1}{2}x$ units
$2x$ units
$xsqrt{2}$ units

Explanation:

Step1: Recall volume formula for prism

The volume formula for a prism is $V = Bh$, where $B$ is the base - area and $h$ is the height. For a square base with edge - length $x$, the base - area $B=x^{2}$.

Step2: Substitute values into formula

We know that $V=\frac{1}{2}x^{3}$ and $B = x^{2}$. Substituting into $V = Bh$ gives $\frac{1}{2}x^{3}=x^{2}h$.

Step3: Solve for $h$

To solve for $h$, divide both sides of the equation $\frac{1}{2}x^{3}=x^{2}h$ by $x^{2}$. When we divide $\frac{1}{2}x^{3}$ by $x^{2}$, using the rule $\frac{x^{m}}{x^{n}}=x^{m - n}$, we have $\frac{\frac{1}{2}x^{3}}{x^{2}}=\frac{1}{2}x^{3-2}=\frac{1}{2}x$. So, $h=\frac{1}{2}x$.

Answer:

$\frac{1}{2}x$ units