Circle A has a radius of 3n and circle B has a radiusof n129 , where n is a positive constant. The area ofcircle B is how many times the area of circle A?A) 43B) 86C) 129D) 1,849
Question
Circle A has a radius of 3n and circle B has a radiusof n129 , where n is a positive constant. The area ofcircle B is how many times the area of circle A?A) 43B) 86C) 129D) 1,849
Solution
The area of a circle is given by the formula πr², where r is the radius of the circle.
For circle A, with radius 3n, the area is π(3n)² = 9πn².
For circle B, with radius n129, the area is π(n129)² = 16641πn².
To find out how many times the area of circle B is the area of circle A, we divide the area of circle B by the area of circle A:
16641πn² / 9πn² = 1849.
So, the area of circle B is 1849 times the area of circle A. The answer is D) 1,849.
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