A Circle With Two Radii

[kittenfelidae]

Please find attached the question along with my workings so far. Please solve it for me and explain to me how I should have approached the problem. Thank you

 

[lev888]

We won't solve it solve it for you.
You found the expression for the area of the first region. What about the second, considering the sum of the 2 areas it's the area of the circle?
After that set up an equation using the given ratio. It will probably simplify to provide the answer.

 

[kittenfelidae]

We won't solve it solve it for you.
You found the expression for the area of the first region. What about the second, considering the sum of the 2 areas it's the area of the circle?
After that set up an equation using the given ratio. It will probably simplify to provide the answer.

Thank you so much. I was confused because the question was not specific. Your answer made me see the logic behind