SAT Question 42155bac: Area and Volume answer and explanation with Desmos solution

Choice A is correct. The volume, $V$, of a right circular cylinder is given by the formula $V=\pi r^{2}h$, where $\pi r^2$ is the area of one of the bases of the cylinder and $h$ is the height. It’s given that the area of one of the bases of the cylinder is $81$ square centimeters and that the volume of the cylinder is $2,187$ cubic centimeters. Substituting $2,187$ for $V$ and $81$ for $\pi r^2$ in the formula $V=\pi r^{2}h$ yields $2,187=81h$. Dividing both sides of this equation by $81$ yields $27=h$. Therefore, the height, in centimeters, of the cylinder is $27$.