Luciano wrote:
Very simple way to solve this problem
Assume : Smaller circle area is 9
Then : Shaded region area is 3 times the area of smaller region therefore -> 27
Therefore : Whole circle area is 36 ( Adding the smaller and the shaded region)
Now radius of whole circle is 6 (Since area is 36)
and radius of smaller circle is 3 (Since area is 9)
Therefore the circumference of the bigger circle is 2* the circumference of the smaller circle.
2*6*pi -> bigger circle & 2*3*pi smaller circle
I like your way of solving, and shaped it.
Let, Smaller circle area is 9,
Then the Shaded region area is \(= 9*3=27\) [Three times the area of the smaller region]
Area of the larger circle (whole circle) \(= 9+27=36\)
∴ The are of the larger circle \(πR^2=36, \ or \ πr=6\), or The perimeter \(2πR=12\)
The are of the smaller circle \(πr^2=9, \ or \ πr=3\), or The perimeter \(2πr=6\)
\( \frac{The \ perimeter \ of \ the \ larger \ circle \ 2πR =12}{ The \ perimeter \ of \ the \ smaller \ circle \ 2πr =6}=2\)
The answer is \(C\)