an oblique cone has a height equal to the diameter of the base. the volume of the cone is equal to 18π cubic…

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Given that the diameter of the base is $2x$ (so the radius $r = x$) and the height $h=2x$, and $V = 18\pi$.

Step2: Substitute values into formula

Substitute $r=x$, $h = 2x$ and $V=18\pi$ into $V=\frac{1}{3}\pi r^{2}h$. We get $18\pi=\frac{1}{3}\pi x^{2}(2x)$.

Step3: Simplify the equation

First, simplify the right - hand side: $\frac{1}{3}\pi x^{2}(2x)=\frac{2}{3}\pi x^{3}$. So the equation becomes $18\pi=\frac{2}{3}\pi x^{3}$. Divide both sides of the equation by $\pi$ (since $\pi\neq0$), we have $18=\frac{2}{3}x^{3}$.

Step4: Solve for x

Multiply both sides of the equation $18=\frac{2}{3}x^{3}$ by $\frac{3}{2}$ to get $x^{3}=27$. Then take the cube - root of both sides, $x = 3$. Since the radius $r=x$, the radius of the cone is 3 units.

Answer:

B. 3 units