SAT Question 5afbdc8e: Area and Volume answer and explanation with Desmos solution

Choice C is correct. The area $A$ of a circle with radius $r$ is given by the formula $A=\pi r^2$. Thus, a circle with radius $2$ has area $\pi \times 2^2$, which can be rewritten as $4\pi$. The area of a square with side length $s$ is given by the formula $A=s^2$. Thus, if a square has the same area as a circle with radius $2$, then $s^2=4\pi$. Since the side length of a square must be a positive number, taking the square root of both sides of $s^2=4\pi$ gives $s=\sqrt{4\pi }$. Using the properties of square roots, $\sqrt{4\pi }$ can be rewritten as $\sqrt{4}\sqrt{\pi }$, which is equivalent to $2\sqrt{\pi }$. Therefore, $s=2\sqrt{\pi }$.