A dartboard consists of two concentric circles. The probability of hitting the inner circle is 16%. If the outer circle has a diameter of 20 inches, what is the radius of the inner circle?

Question

anonymous · Answer

5:) because the radius to the big circle is the diameter to the samll one. Take half of the small diameter and u get 5... hope this helps:)

anonymous · Answer

The answer choices are 2,4,8 and 16

anonymous · Answer

ok wait i totally messed tht up...SORRY

anonymous · Answer

ok sry maybe u should take @jim_thompson5910  help... sorry

jim_thompson5910 · Answer

You first need to find the area of the larger circle.


The larger circle has a diameter of 20, or a radius of 20/2 = 10


So what is the area of this larger circle?

anonymous · Answer

100pi?

jim_thompson5910 · Answer

good, so if the probability of landing in the smaller circle is 16%, then this means

P(Landing in Smaller Circle) = (Area of Smaller Circle)/(Area of Larger Circle)

16/100 = x/(100pi)

cross multiply and solve for x to get

16/100 = x/(100pi)

16*100pi = 100x

1600pi = 100x

100x = 1600pi

x = 1600pi/100

x = 16pi

Which means that the area of the smaller circle is 16pi square inches

jim_thompson5910 · Answer

now that you know the area of the smaller circle is 16pi, you can use this to find the radius of the inner circle

jim_thompson5910 · Answer

how do we do this?

anonymous · Answer

divide it by 2?

jim_thompson5910 · Answer

Remember that 

A = pi*r^2

is the area of a circle

jim_thompson5910 · Answer

So

A = pi*r^2

16pi = pi*r^2

16 = r^2  ... Divide both sides by pi.

r^2 = 16

r = ???

anonymous · Answer

r=4?

jim_thompson5910 · Answer

you got it

anonymous · Answer

Thank you :D

jim_thompson5910 · Answer

np