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Circle $A$ has a radius of $3n$ and circle $B$ has a radius of $129n$, where $n$ is a positive constant. The area of circle $B$ is how many times the area of circle $A$?

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Circle $A$ has a radius of $3n$ and circle $B$ has a radius of $129n$, where $n$ is a positive constant. The area of circle $B$ is how many times the area of circle $A$?

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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 $A=\\pi(3n)^{2}$, 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 $A=\\pi(129n)^{2}$, 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 $A$.

Choice A is incorrect. This is how many times greater the radius of circle $B$ is than the radius of circle $A$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the coefficient on the term that describes the radius of circle $B$.

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Circle $A$ has a radius of $3n$ and circle $B$ has a radius of $129n$, where $n$ is a positive constant. The area of circle $B$ is how many times the area of circle $A$?

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129

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1,849

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