An archery target has three concentric circular regions. The diameters

1.	An archery target has three concentric circular regions. The diameters of the regions are in the ratio1:2:3. Find the ratio of their areas
Answer» Then the radii are d/2, d, 3d/2 The area of the central circle = pi.d^2/4 The area of the next region = pi (d^2 - d^2/4) = (3/4)pi.d^2 The area of the outermost region = pi (9d^2/4 - d^2) = (5/4)pi.d^2 Cancel out the 1/4ths So the ratios of their areas are: 1:3:5

An archery target has three concentric circular regions. The diameters of the regions are in the ratio1:2:3. Find the ratio of their areas

Answer»

Then the radii are d/2, d, 3d/2

The area of the central circle = pi.d^2/4

The area of the next region = pi (d^2 - d^2/4) = (3/4)pi.d^2

The area of the outermost region = pi (9d^2/4 - d^2) = (5/4)pi.d^2

Cancel out the 1/4ths

So the ratios of their areas are: 1:3:5