SAT Question 3b931fb0: Area and Volume answer and explanation with Desmos solution

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. Since the base of the cylinder is a circle with radius $r$, the area of the base of the cylinder is $\pi r^2$. It's given that a right circular cylinder has a volume of $377$ cubic centimeters; therefore, $V=377$. It's also given that the area of the base of the cylinder is $13$ square centimeters; therefore, $\pi r^2=13$. Substituting $377$ for $V$ and $13$ for $\pi r^2$ in the formula $V=\pi r^{2}h$ yields $377=13h$. Dividing both sides of this equation by $13$ yields $29=h$. Therefore, the height of the cylinder, in centimeters, is $29$.