SOLUTION: Three concentric circles are drawn such that the area of the smallest circle is equal to the area of each of the rings. If the radius of the largest circle is 12cm, what is the rad

Question 1133859: Three concentric circles are drawn such that the area of the smallest circle is equal to the area of each of the rings. If the radius of the largest circle is 12cm, what is the radius of the smaller circle?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
If one draws this, it may be seen that the area of the small circle plus the area of the two rings equals the area of the large circle.
The area of the large circle is 144 pi cm^2, from pi*r^2
The area of each of the rings is equal to that of the small circle, so the area of all three (circle and two rings) is 144pi cm^2, and since the three are equal, the area of the small circle is 48 pi cm^2
That means 48 pi cm^2=pi* r^2
so r^2=48
r= sqrt (48) or 4 sqrt (3) cm or about 6.9 cm

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