SAT Question 179edb12: Area and Volume answer and explanation with Desmos solution

It’s given that the right circular cone has a height of $22$ cm and a base with a diameter of $18$ cm. Since the diameter of the base of the cone is $18$ cm, the radius of the base is $9$ cm. The volume $V$, in ${\text{cm}}^3$, of a right circular cone can be found using the formula $V=\frac{1}{3}\pi r^{2}h$, where $h$ is the height, in $\text{cm}$, of the cone and $r$ is the radius, in $\text{cm}$, of the base of the cone. Substituting $22$ for $h$ and $9$ for $r$ in this formula yields $V=\frac{1}{3}\pi {\left(9\right)}^2(22)$, or $V=594\pi$. Therefore, the volume of the cone is $594\pi {\text{cm}}^3$. It’s given that the volume of the cone is $n\pi {\text{cm}}^3$. Therefore, the value of $n$ is $594$.