Problem D

Coloured Areas

Chandra wishes to paint a sign. The sign is composed of three concentric semi-circles, creating an outer band, a middle band, and an inner semi-circle.

The outer band is divided into five regions of equal area and will be painted blue. Each of these regions is labelled with a \(B\). The middle band is divided into three regions of equal area and will be painted red. Each of these regions is labelled with an \(R\). The inner semi-circle will be painted white.

The diameter of the largest semi-circle is \(10\) m and the diameter of the middle semi-circle is \(6\) m.

If the ratio of the area of one region marked with an \(R\) to the area of one region marked with a \(B\) is \(5:6\), what is the diameter of the inner semi-circle?