SAT Question deff8a2f: Area and Volume answer and explanation with Desmos solution

Choice C is correct. The volume, $V$, of a right circular cylinder is given by the formula $V=\pi r^{2}h$, where $r$ is the radius of the base of the cylinder and $h$ is the height of the cylinder. It's given that a right circular cylinder has a height of $6$ meters. Therefore, $h=6$. It's also given that the right circular cylinder has a base with a circumference of $20\pi$ meters. The circumference, $C$, of a circle is given by $C=2\pi r$, where $r$ is the radius of the circle. Substituting $20\pi$ for $C$ in the formula $C=2\pi r$ yields $20\pi =2\pi r$. Dividing each side of this equation by $2\pi$ yields $10=r$. Substituting $10$ for $r$ and $6$ for $h$ in the formula $V=\pi r^{2}h$ yields $V=\pi (10{)}^2\left(6\right)$, or $V=600\pi$. Therefore, the volume, in cubic meters, of the cylinder is $600\pi$.