Question

the base diameter and the height of a cone are both equal to x units. which expression represents the volume of the cone, in cubic units? o $pi x^{2}$ o $2pi x^{3}$ o $\frac{1}{3}pi x^{2}$ o $\frac{1}{12}pi x^{3}$

Explanation:

Step1: Find the radius of the cone

The diameter $d = x$, so the radius $r=\frac{d}{2}=\frac{x}{2}$.

Step2: Recall the volume formula of a cone

The volume formula of a cone is $V = \frac{1}{3}\pi r^{2}h$.

Step3: Substitute the values of $r$ and $h$ into the formula

Here $r=\frac{x}{2}$ and $h = x$. So $V=\frac{1}{3}\pi(\frac{x}{2})^{2}\cdot x$.

Step4: Simplify the expression

$V=\frac{1}{3}\pi\cdot\frac{x^{2}}{4}\cdot x=\frac{1}{12}\pi x^{3}$.

Answer:

$\frac{1}{12}\pi x^{3}$