Question

An archery target has three concentric regions. The diameters of the regions are in the ratio 1:2:3. Find the ratio of their areas

Answer 1

The area of central circle would be : pi. d^2 /4

the area of the next region would be :  pi ( d^2  - d^2/4) = 3/4 pi d^2

The outermost region would be : pi (9d^2 / 4 - d^2/4) = 5/4 pi d^2

Just multiply all equation with 4, you will get that the ratio will become 1 : 3 : 5

Hope this helps