If r is the radius (a linear measurement) of a room, then the ratio of the areas A (a square measurement) is the square of the ratios of the radii. The ratio of the radii is 6y:3y=2:1. When we square the ratio we get 4:1, so Room 1 has 4 times the area of Room 2. The ratio small:large is 1:4.
Note that the rooms don't have to be circular as long as the shapes are similar. Two circles have the same shape; two squares have the same shape; two equilateral triangles have the same shape; two equilateral polygons have the same shape. r could be the side of a square, the radius of a circle, the side of an equilateral triangle, etc. It is just one linear measurement indicating the size. A rectangular room would need two measurements if the rooms were the same height.