SAT Question f329442c: Area and Volume answer and explanation with Desmos solution

Choice D is correct. The area of a circle can be found by using the formula $A=\pi r^2$, where $A$ is the area and $r$ is the radius of the circle. It's given that the radius of circle A is $3n$. Substituting this value for $r$ into the formula $A=\pi r^2$ gives $A=\pi {\left(3n\right)}^2$, or $9\pi n^2$. It's also given that the radius of circle B is $129n$. Substituting this value for $r$ into the formula $A=\pi r^2$ gives $A=\pi {\left(129n\right)}^2$, or $16,641\pi n^2$. Dividing the area of circle B by the area of circle A gives $\frac{16,641\pi n^2}{9\pi n^2}$, which simplifies to $1,849$. Therefore, the area of circle B is $1,849$ times the area of circle A.