a The board has a radius of 4 units. What about the unshaded part?
B
b The unshaded part can be determined by using the calculations from Part A.
A
a 1/4
B
b 1/3
Practice makes perfect
a The probability of a dart hitting the dartboard at random, and landing in the unshaded region, is given by the following ratio.
P(unshaded area)=A_(unshaded)/A_(board)
Therefore, we must calculate the area of the entire board and the unshaded part of the board. To do this we need to know these circle's respective radius.
With this information, we can calculate the area of each circle.
|c|c|c|c|
[-0.8em]
Part & r & π r^2 & Area [0.5em]
[-0.8em]
Unshaded & 2 & π( 2)^2 & 4π [0.5em]
[-0.8em]
Board & 4 & π( 4)^2 & 16π [0.5em]
When we know the area of each part, we can calculate the probability of a dart landing in the unshaded region.
P(unshaded area)=4Ď€/16Ď€=1/4
b Like in Part A, we have to divide the unshaded area by the boards area. From Part A, we have calculated the area of circle's with a radius of 2 and 4 units.
&A_(radius is 2) = 4 units^2
&A_(radius is 4) = 16 units^2
Now we can determine the area of the unshaded part of the board in Part B to 16π -4π =12 π.
From the diagram, we see that the board is a circle with a radius of r= 6 units. With this information, we can calculate its area.
A_(board) =Ď€( 6)^2 = 36Ď€
Now we have enough information to calculate the probability of hitting the unshaded region.
P(unshaded area)=12Ď€/36Ď€=1/3
