The area of a circular ring enclosed between two concentric circles is $286 {\mathrm{cm}}^2$. Find the radii of the two circles if their difference is $7 \mathrm{cm}$.

The figure shows an archery target marked with its five scoring areas from the centre outward as Gold, Red, Blue, Black and White. The diameter of the region representing Gold is $21 \mathrm{cm}$ and each of the other band is $10.5 \mathrm{cm}$ wide. Find the area of each of the five scoring regions.