Question

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? a) 43 b) 86 c) 129 d) 1,849

Explanation:

Step1: Recall circle area formula

The area of a circle is $A = \pi r^2$, where $r$ is the radius.

Step2: Calculate area of Circle A

Substitute $r=3n$ into the formula:
$A_A = \pi (3n)^2 = 9\pi n^2$

Step3: Calculate area of Circle B

Substitute $r=129n$ into the formula:
$A_B = \pi (129n)^2 = 16641\pi n^2$

Step4: Find the ratio $A_B/A_A$

Divide $A_B$ by $A_A$ to find the multiple:
$\frac{A_B}{A_A} = \frac{16641\pi n^2}{9\pi n^2} = 1849$

Answer:

D) 1,849