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An archery target has three regions formed by three concentric circles as shown in the figure. If the diameters of the concentric circles are in the ratio 1: 2: 3, then find the ratio of the areas of three regions.

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3:5:4

1:7:9

2:5:4

1:3:5

answer is D.

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Detailed Solution

Given that the diameters of the concentric circles are in the ratio 1: 2: 3.
We have to find the ratio of the areas of three regions.
Let the diameters of the concentric circles be s, 2s and 3s.
Then their radii are

s 2

2 s 2 = s

and

3 s 2

.
Therefore, the area of the first circle,

A 1

is,

A 1 = π s 2 2 ⇒ A 1 = π s 2 4

The area of the second circle,

A 2

A 2 = π s 2

And the area of the third circle,

A 3

A 3 = π 3 s 2 2 ⇒ A 3 = 9 π s 2 4

. Area enclosed between first and second circle,

A'

is,

A' = π s 2 − π s 2 4 ⇒ A' = 3 π s 2 4

.
Area enclosed between by the second and third circle,

A''

is,

A'' = 9 π s 2 4 − π s 2 ⇒ A'' = 5 π s 2 4

.
So, the ratio of the areas of three regions is,

π s 2 4 : 3 π s 2 4 : 5 π s 2 4 = 1 : 3 : 5

.
The ratio of the areas of three regions is

1 : 3 : 5

.
Therefore, the correct option is 4.

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