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?

Answer 1

3 times more.

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
`\pi r^(2)`.

• inner circle:
  `A=\pi 2^(2)=12.566`
• for the outer circle, use the formula then subtract the value of the inner circle, to find the remaining area:
  `A=(\pi 4^(2) )-12.566=37.699`

Calculating greater chance:

Divide the larger area by the smaller area:

`37.699/12.566 = 3`

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.