The diagram shows a logo made from three circles - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 1

The radius of the middle circle is 3 cm. Using the same area formula:

$A = ext{π}(3)^2 = 9 ext{π} ext{ cm}^2$

The shaded area corresponds to the area of the largest circle minus the area of the middle circle:

$ext{Shaded Area} = 16 ext{π} - 9 ext{π} = 7 ext{π} ext{ cm}^2$

Next, we need to find the total area of the logo, which is the area of the largest circle:

$ext{Total Area} = 16 ext{π} ext{ cm}^2$

To find out if the shaded area is indeed rac{1}{3} of the total area:

rac{1}{3} imes 16 ext{π} = rac{16 ext{π}}{3} ext{ cm}^2

Comparing this with the shaded area of $7 ext{π} ext{ cm}^2$:

Since $7 ext{π}$ is approximately $21.99$, and rac{16 ext{π}}{3} is approximately $16.76$, we conclude that Daisy is wrong: the shaded area is not rac{1}{3} of the logo.