Ratio of diameter is 1 : 2

So ratio of radius is also 1 : 2

Let the smaller circle's radius be u (or 1u, they are effectively the same)

Then bigger circle's radius is 2u.


Area of smaller circle
= πr²
= π × u × u
(Or πu²)


Area of bigger circle
= πr²
= π × 2u × 2u
= π × 2 × u × 2 × u
= π × 2 × 2 × u × u
= π × 4 × u × u
(Or 4πu²)


So we can see that the bigger circle's area is 4 times of the smaller circle's area.


Since the area of the smaller circle is 42cm², the bigger circle's area is 4 times of that.

This also tells you that the shaded area is 3 times of that.


So 42cm² × 3 = 126cm²