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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Accepted Answer

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