6. If the diameters of the concentric circlesshown in the figure below

1.	6. If the diameters of the concentric circlesshown in the figure below are in the ratio 1:2:3 then find the ratio of the areas of threeregions.
Answer» Let radius of three concentric circles are r, 2r, 3r Area of first region A1= pirr Area of second region A2= pi2r2r - pirr= 3pirr Area of third region A3= pi3r3r - pi2r2r= 5pirr Ratio of area of three regions areA1:A2:A3 = pirr:3pirr:5pirr= 1:3:5

6. If the diameters of the concentric circlesshown in the figure below are in the ratio 1:2:3 then find the ratio of the areas of threeregions.

Answer»

Let radius of three concentric circles are r, 2r, 3r

Area of first region A1= pi*r*r

Area of second region A2= pi*2r*2r - pi*r*r= 3pi*r*r

Area of third region A3= pi*3r*3r - pi*2r*2r= 5pi*r*r

Ratio of area of three regions areA1:A2:A3 = pi*r*r:3pi*r*r:5pi*r*r= 1:3:5