Circle A has a radius of 3 n and circle B has a radius of 129 n , where n

Question

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

Accepted Answer

Choice D is correct. The area of a circle can be found by using the formula A = r 2 , where A is the area and r is the radius of the circle. It&rsquo;s given that the radius of circle A is 3 n . Substituting this value for r into the formula A = r 2 gives A = 3 n 2 , or 9 n 2 . It&rsquo;s also given that the radius of circle B is 129 n . Substituting this value for r into the formula A = r 2 gives A = 129 n 2 , or 16,641 n 2 . Dividing the area of circle B by the area of circle A gives 16,641 n 2 9 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 .

Question circle