OG详解-OG8 数学1 Q18

Choice D is correct. The area of a circle can be found by using the formula A = πr², 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 = πr² gives A = π (3n)² , or 9πn². It’s also given that the radius of circle B is 129n. Substituting this value for r into the formula A = πr²  gives A = π (129n)² , or 16,641πn². Dividing the area of circle B by the area of circle A gives 16641π²​9π^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.