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?

Question

30-07-2019
Mathematics

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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?

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jessicapieterse jessicapieterse · Answer 1 · 2019-08-06T14:30:39+02:00

Answer:

3 times more.

Step-by-step explanation:

The odds of landing a dart in any of the circles correspond to the surface area of the circle.

Calculate the surface area of both circles:

The formula for the area of a circle is [tex]\pi r^{2}[/tex].

inner circle: [tex]A=\pi 2^{2}=12.566[/tex]
for the outer circle, use the formula then subtract the value of the inner circle, to find the remaining area: [tex]A=(\pi 4^{2} )-12.566=37.699[/tex]

Calculating greater chance:

Divide the larger area by the smaller area:

[tex]37.699/12.566 = 3[/tex]

That means that the area of the outer circle is 3 times larger, making it 3 times more likely to hit the outer circle. Therefore the points for hitting the inner circle should be 3 times more.