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

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 $\pi r^{2}$.

• 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.