A dartboard has three concentric circles and the radius of the inner circle is 1. If the probability of landing in each of the three regions is the same, find the EXACT value of the radii of the other two circles. SHOW WORK!

Question

jack1 · Answer

therefore the area of each circle is the same
so A of Circle = pi x r^2

jack1 · Answer

area of 2nd circle = (pi x r^2) - area of circle 1

jack1 · Answer

area of 3rd circle = (pi x r^2) - (area of circle 1 + area of circle 2)

jack1 · Answer

as circles have equal area:
Area of circle 1= area of circle 2 = area of circle 3

anonymous · Answer

What is the area?

jack1 · Answer

you have the radius, you tell me

anonymous · Answer

Well pi (1)2 is 1pi so they are all 1pi?

jack1 · Answer

yep, perfect

anonymous · Answer

Huh, that was more simple than I thought. Thank you very much.

jack1 · Answer

the q was to find out the radius tho

jack1 · Answer

so radius of circle 1 is given : 1

jack1 · Answer

radius of circle 2 is...
area of 2nd circle = (pi x r^2) - area of circle 1 
3.14 = (pi x r^2) - 3.14
2 pi = pi x r^2
2 = r^2
r = sqr rt of 2

jack1 · Answer

following ok so far?

jack1 · Answer

so tell me what you get for radius of circle 3?

anonymous · Answer

Urm, do you subtract 3.14 from the area of the first and second circle?

jack1 · Answer

start with this equation:
area of 3rd circle = (pi x r^2) - (area of circle 1 + area of circle 2)

jack1 · Answer

sub in 3.14 wherever you see "area of circle #"

anonymous · Answer

3pi = pir2
3pi = r^2?
r= sqr of 3?

jack1 · Answer

perfect!

jack1 · Answer

your second line's a typo, yeah?
its supposed to read 3 = r^2?

anonymous · Answer

Yeah, opps.

jack1 · Answer

all good, well done

anonymous · Answer

Thank you so much for helping. That was very simple and easy :).

jack1 · Answer

was a pleasure