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 prism with edge length $x$ units, the base - area $B=x\times x=x^{2}$ square units.

Step2: Substitute values into formula

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

Step3: Solve for $h$

To find $h$, divide both sides of the equation $\frac{1}{2}x^{3}=x^{2}h$ by $x^{2}$ (assuming $x
eq0$). Using the rule of exponents $\frac{x^{m}}{x^{n}}=x^{m - n}$, we have $h=\frac{\frac{1}{2}x^{3}}{x^{2}}$. Since $\frac{x^{3}}{x^{2}}=x^{3-2}=x$, then $h = \frac{1}{2}x$ units.

Answer:

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