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?

Explanation

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(3n2) , 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 16,641πn2 / 9πn2, which simplifies to 1,849. Therefore, the area of circle B is 1,849 times the area of circle A.