A simple dart target has two concentric circles. The larger circle has a radius of 4. The smaller circle has a radius of 2.

The scoring should correspond to the relative difficulty of hitting the inner circle and the outer ring. How many more points should a player receive for landing a dart in the inner circle, as opposed to the outer ring?

The player should receive 4π times as many points.
The player should receive 2π times as many points.
The player should receive 9 times as many points.
The player should receive 3 times as many points.

Question

A simple dart target has two concentric circles. The larger circle has a radius of 4. The smaller circle has a radius of 2.

The scoring should correspond to the relative difficulty of hitting the inner circle and the outer ring. How many more points should a player receive for landing a dart in the inner circle, as opposed to the outer ring?

The player should receive 4π times as many points.
The player should receive 2π times as many points.
The player should receive 9 times as many points.
The player should receive 3 times as many points.

anonymous · Answer

Well the probability of hitting either ring is directly proportional to each rings area.
We know that both rings are essentially circles, however the outer circle must subtract the area of the inner circle. 
You should also know that the area of a circle is A = pi*r^2
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Now the points should be inversely proportional to the area (since smaller areas are harder to hit and should be worth more points), and we just need to take a ratio of the two areas:

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